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343.WooDROw,    Herbert.     Brightness    and    Dullness    in    Children. 

Philadelphia:    J.  B.  Lippincott  and  Company,  1919.    322  p. 

There  are  various  discussions  of  retardation  and  advancement,  elimination, 
special  classes,  bright  and  dull  pupils  and  experiments  with  bright  pupils. 

344.W00DS,  Elizabeth  L.  "Provision  for  the  gifted  child,"  Edu- 
cational Administration  and  Supervision,  3:139-49,  March,  1917. 

A  summary  of  provisions  in  a  large  number  of  cities  showing  that  flexible 
promotion  is  ver>'  common,  special  classes  or  groups  fairly  so,  and  that  practically 
all  superintendents  favor  making  some  such  provision. 

345.  Young,  Ella  Flagg.  "Grading  and  classification  of  pupils,"  Ad- 
dresses and  Proceedings  of  the  National  Educational  Associa- 
tion, 32:83-86,  1893. 

A  rather  general  discussion. 

346.  "The  Cambridge  plan,"  Journal  of  Education,  75:375-76,  April 
4,  1912. 

A  brief  description  of  this  plan. 


[50] 


BULLETIN  No.  17 


BUREAU  OF  EDUCATIONAL  RESEARCH 
COLLEGE  OF  EDUCATION 


THE  PRESENT 

STATUS  OF  WRITTEN  EXAMINATIONS 

AND  SUGGESTIONS  FOR  THEIR 

IMPROVEMENT 


By 


Walter  S.  Monroe 

Director,   Bureau  of  Educational  Research 

Assisted  by 

Lloyd  B.  Souders 
Formerly  Assistant  in  Bureau  of  Educational  Research 


PRICE    SO   CENTS 


PUBLISHED  BY  THE  UNIVERSITY  OF  ILLINOIS,  URBANA 

1923 


TABLE  OF  CONTENTS 


PAGE 

Preface 5 

Chapter  I. — Introduction 7 

Chapter  II. — Summary  of  criticisms  of  written  examina- 
tions    9 

Examinations  yield  inaccurate  measures  of  school  achieve- 
ment   9 

Written    examinations    tend     to    encourage     undesirable 

mental  processes 13 

Passing  the  final  examination  an  undesirable  objective.  ...  14 

Examinations  injurious  to  health  of  students 14 

Time  devoted  by  teachers  to  written  examinations    not 

profitably  spent 15 

Chapter  III. — Preparation  and  administration  of  exam- 
inations IN  HIGH  school 16 

The  data  collected 16 

Requirement  of  final  examinations  in  Illinois  high  schools  16 

Time  devoted  to  written  examinations 19 

Characteristics  noted  in  marking  examination  papers 20 

Weighting  of  questions 22 

Recognition  of  rate  of  work 22 

Methods  of  marking  examination  papers 23 

Directions  to  students  concerning  methods  of  work 24 

Recognition  of  a  standard  distribution  in  assigning  grades 

to  examination  papers 24 

Relation  of  examination  grades  to  final  grades 25 

Summary 25 


Chapter  IV. — The  constant  and  variable  errors  in  exam- 
ination  GRADES 27 

Constant  and  variable  errors  of  measurement 27 

Magnitude  of  variable  errors   of  measurement  in   stand- 
ardized test  scores  and  in  examination  grades 28 

Methods   employed    in    present    investigation    concerning 
reliability  of  written  examinations 29 

Data  collected  for  investigation 30 

Reliability  of  written   examination  grades  and  of  stand- 
ardized test  scores 31 

Conditions  tending  to  produce  variable  errors  of  measure- 
ment in  examination  grades 37 

Magnitude  of  constant  errors  of  measurements  in  stand- 
ardized test  scores  and  in  examination  grades 40 

Results  of  present   investigation  and  of  previous  studies 
compared 41 

Conclusion — relative  accuracy  of  examination  grades  and 
of  test  scores 41 

Chapter  V. — The  content  of  written  examinations 43 

The  data  collected 43 

Classification  of  questions 43 

Relation    of   examination    questions     to    educational    ob- 
jectives       46 

Chapter  VI. — The  improvement  of  written  examinations.     48 

Reduction  of  constant  errors 50 

Reduction  of  variable  errors 54 

Agreement  of   content  of  examinations  with  educational 
objectives 55 

Simplification  of  administration  of  written  examinations.  .      56 

Chapter  VII. — Rules  for  the   preparation   and  adminis- 
tration OF  written    examinations 63 

Appendix 66 


PREFACE 

This  bulletin  reports  the  results  of  three  extensive 
investigations  relating  to  written  examinations.  These 
investigations  were  made  by  Mr.  Souders  under  the  di- 
rection of  the  Director  of  the  Bureau  of  Educational  Re- 
search. The  tabulations  and  statistical  calculations  were 
made  by  Mr.  Souders  or  by  clerks  working  under  his  im- 
mediate direction.  The  preparation  of  the  published  re- 
port, however,  is  the  work  of  the  Director  of  the  Bureau. 

The  Bureau  of  Educational  Research  wishes  to  ac- 
knowledge its  indebtedness  to  the  superintendents,  prin- 
cipals, and  teachers  who  cooperated  by  furnishing  the 
necessary  data.  The  data  required  in  the  study  of  relia- 
bility of  written  examinations  necessitated  considerable 
additional  labor.  Without  their  cooperation  these  in- 
vestigations would  not  have  been  possible. 

Walter  S.  Monroe,  Director. 
November  1,  1923. 


Digitized  by  the  Internet  Archive 

in  2011  with  funding  from 

University  of  Illinois  Urbana-Champaign 


http://www.archive.org/details/presentstatusofw17monr 


PRESENT  STATUS  OF  WRITTEN  EXAMINATIONS 

AND  SUGGESTIONS  FOR  THEIR 

IMPROVEMENT 

CHAPTER  I 
INTRODUCTION 

Preparation  and  administration  of  written  examinations  im- 
portant phases  of  the  teacher's  work.  Written  examinations, 
except  in  tlie  few  schools  where  they  have  been  abolished,  form  a 
very  important  phase  of  the  teacher's  work,  both  because  of  the 
time  devoted  to  their  preparation  and  administration  and  of  the 
significance  attached  to  the  measures  which  they  yield.  The  final 
grades  upon  which  promotion  and  the  awarding  of  school  honors 
depend  are  determined  largely  by  final  examinations  and  by  writ- 
ten tests  given  during  the  school  term.  Altho  standardized  edu- 
cational tests  have  become  widely  used  during  recent  years, 
written  examinations  are  still  the  most  frequently  used  type  of 
measuring  instrument.  This  will  probably  always  be  true,  par- 
ticularly in  the  high  school.  Hence,  we  may  expect  that  written 
examinations  will  occupy  in  the  future  as  in  the  past,  an  important 
place  in  the  work  of  our  schools. 

Need  for  more  information  concerning  written  examinations. 
Thefl^have  been  numerous  investigations  which  showed  that 
the  marking  of  written  examination  papers  is  highly  subjective — 
that  is,  different  teachers  tend  to  assign  different  marks  to  the 
same  paper.  With  the  exception  of  these  studies  relatively  little 
precise  information  is  available  in  regard  to  written  examinations 
but  a  number  of  criticisms  based  upon  experience  and  theoretical 
considerations  have  been  made.  As  a  result  many  teachers  and 
other  school  officials  have  come  to  consider  written  examinations 
very  inferior  instruments  and  have  abolished  them  in  a  number  of 
schools. 

A  search  through  our  educational  literature,  particularly 
textbooks,  reveals  an  astonishing  lack  of  information  in  regard  to 
written  examinations.   Relatively  little  specific  attention  has  been 

[7] 


given  to  their  preparation  and  administration  in  our  courses  for 
the  training  of  teachers.  Inexperienced  teachers  have  been  left 
largely  to  their  own  devices  in  this  important  phase  of  their  work. 
Careful  inquiry  and  observation  have  indicated  that  there  is  a  variety 
of  practises  with  reference  to  the  types  of  questions  asked  and 
to  the  administration  of  written  examinations.  Hence  it  appears 
that  there  is  need  for  a  comprehensive  investigation  of  the  present 
status  of  written  examinations  in  order  that  a  more  intelligent  esti- 
mate may  be  formed  of  their  value  in  the  process  of  education  and 
that  specific  directions  may  be  formulated  in  regard  to  their 
preparation  and  administration. 

Purpose  of  this  bulletin.  It  is  the  purpose  of  this  bulletin  to 
present  (1)  a  brief  summary  of  certain  previous  investigations  re- 
lating to  written  examinations  and  also  of  the  arguments  for  and 
against  written  examinations;  (2)  the  results  of  three  extensive  in- 
vestigations conducted  by  the  Bureau  of  Educational  Research, 
(a)  the  preparation  and  administration  of  written  examinations  in 
Illinois  high  schools,  (b)  the  constant  and  variable  errors  in  exami- 
nation grades,  and  (c)  the  content  of  written  examinations;  and 
(3)  suggestions  for  the  improvement  of  written  examinations.  In 
the  concluding  chapter  the  author  presents  a  list  of  rules  in  regard 
to  the  preparation  and  administration  of  written  examinations. 


[8] 


CHAPTER  II 

SUMMARY  OF  CRITICISMS  OF  WRITTEN  EX- 
AMINATIONSi 

Plan  of  chapter.  In  this  chapter  the  important  criticisms  of 
written  examinations  are  briefly  summarized.  Following  each 
criticism  either  a  brief  answer  is  given  or  a  reference  is  made  to  a 
detailed  discussion  in  a  later  chapter.  By  presenting  both  sides 
of  the  question  in  this  way,  it  is  hoped  that  the  reader  will  be 
assisted  in  forming  an  intelligent  estimate  of  the  merits  of  written 
examinations. 

I.  Examinations  yield  inaccurate  measures  of  school  achieve- 
ment.   In  support  of  this  argument  six  points  have  been  made. 

1.  The  most  important  criticism  relating  to  the  accuracy  of 
written  examinations  is  that  the  marking  of  the  papers  is  highly 
&uly££tiy-£.  A  large  number  of  scientific  investigations  have 
yielded  objective  evidence  that  different  teachers  when  working 
independently  tend  to  assign  widely  varying  marks  to  the  same 
paper.  One  of  the  first  studies  of  this  type  was  by  Starch  and 
Elliott  who  found  that  the  marks  assigned  to  the  same  examina- 
tion paper  in  Plane  Geometry  by  116  teachers  ranged  from  28  to 
92  on  the  scale  of  100  percent.  The  facts  of  such  investigations  as 
this  can  not  be  disputed  but  as  we  have  no  means  of  securing  per- 
fectly accurate  measures  of  achievement,  the  question  at  issue 
concerns  the  relative  rather  than  the  absolute  accuracy  of  the 
measurements  secured.  Facts  may  be  misinterpreted.  In  Chapter 
IV  we  shall  present  evidence  to  show  that  when  judged  in  relation 
to  other  means  for  measuring  school  achievement,  written  exami- 


'Starch,  Daniel,  and  Elliott,  E.  C.  "Reliability  of  grading  high-school  work  in 
mathematics,"    School  Review,  21:254-59,  April,  1913. 

Morton,  Robert  L.  "The  examination  method  of  licensing  teachers,"  Education- 
al Administration  and  Supervision,  6:421,  November,  1920. 

Wood,  Ben  D.  "Measurement  of  college  work,"  Educational  Administration  and 
Supervision,  7:301-34,  September,  1921. 

Kelly,  F.  J.  "Teachers'  marking,"  Teachers  College  Contributions  to  Education, 
No.  66.    New  York:  Teachers  College,  Columbia  University,  1914. 

[9] 


nations  yield  relatively  more  accurate  measures  than  generally 
supposed.  In  view  of  the  additional  information  secured  the  sub- 
jectivity of  written  examinations  loses  much  of  its  potency  as  a 
reason  for  their  abolition. 

2.  The  questions  of  ordinary  examinations  are  usually  not 
equal  in  difficulty  and  weighting  by  teachers  is  highly  subjective.^ 
It  has  been  inferred  that  this  condition  tends  to  increase  mater- 
ially the  inaccuracy  of  examination  marks.  Comparisons  of 
weighted  and  non-weighted  scores  yielded  by  standardized  tests 
have  revealed  that  the  errors  introduced  by  disregarding  the  unequal 
difficulty  of  exercises  or  questions  are  not  significant  in  most  cases.' 

3.  It  has  been  pointed  out  that  frequently  the  content  of 
written  examinations  is  not  in  agreement  with  recognized  educa- 
tional objectives.  Catch  questions  relating  to  trivial  facts  or 
worded  in  a  misleading  way  have  been  cited  as  illustrations. 
Certain  examination  questions  also  have  referred  to  items  which 
had  not  been  included  in  the  course  or  at  least  had  received  only 
minor  emphasis.  Some  evidence  with  reference  to  the  justifica- 
tion of  this  criticism  will  be  presented  in  Chapter  V. 

4.  In  most  examinations  the  rate  of  work  is  neglected.  The 
usual  practise  is  to  allow  sufficient  time  for  all  pupils  to  finish  or 
to  base  the  mark  only  on  the  questions  answered  in  the  unfinished 
papers.  Hence  a  student's  examination  grade  is  not  influenced  by 
the  rate  at  which  he  answers  the  questions.  It  is  easily  possible  to 
take  into  account  the  student's  rate  of  work  in  determining  the 
mark  assigned  to  his  examination  paper.  One  plan  is  to  set  an  ex- 
amination of  sufficient  length  so  that  all  members  of  the  class  will 
be  employed  during  the  entire  period.  Another  procedure  is  to 
have  the  student  record  the  time  when  he  finishes.  In  this  way 
some  weight  can  be  given  to  his  rate  of  work.  This  criticism  is, 
however,  a  minor  one.  In  some  subjects  the  rate  of  work  is  an  im- 
portant consideration  but  in  others,  particularly  those  in  which 
reasoning  predominates  in  answering  the  questions,  the  neglect  of 
the  rate  of  work  will  affect  the  accuracy  of  the  examination  marks 
only  slightly,  if  at  all. 


^Comin,  Robert.  "Teachers'  estimates  of  the  abilities  of  pupils,"  School  and 
Society,  3:67-70,  January  8,  1916. 

'Charters,  W.  W.  "Constructing  a  language  and  grammar  scale,"  Journal  of  Edu- 
cational Research,  1:249-58,  April,  1920. 

Monroe,  Walter  S.  "The  description  of  the  performances  of  pupils  on  exercises 
of  varying  difficulty,"  School  and  Society,  15:341-43,  March,  1922. 

[10] 


5.  Written  examinations  are  usually  so  short  that  they  do  not 
offer  an  adequate  opportunity  for  a  student  to  demonstrate  his 
ability.  This  criticism  is  frequently  expressed  in  the  statement 
that  it  is  unjust  to  base  a  student's  standing  for  a  semester  or  a 
year  on  an  examination  paper  written  during  a  brief  examination 
period.  When  stated  in  this  way  the  criticism  refers  to  two  issues 
between  which  there  is  failure  to  distinguish.  The  first  is  in  regard 
to  the  weight  allowed  the  examination  grades  in  determining  a 
student's  final  standing.  This  question  of  the  weight  given  the 
final  examination  is  discussed  in  a  later  chapter,  but  it  may  be 
said  here  that  the  usual  practise  in  high  schools  is  to  count  the 
written  examination  as  one-third  of  the  student's  total  grade.  The 
second  refers  to  the  inaccuracy  of  the  grade  due  to  the  limited 
opportunity  which  is  given  the  student  to  demonstrate  his  ability. 
For  practical  reasons  it  is  necessary  that  measurement  of  the  total 
achievement  for  the  term  be  based  upon  a  sample.  In  general,  in- 
creasing the  scope  of  the  examination  will  tend  to  increase  the 
accuracy  of  the  measures  yielded.  Some  evidence  with  reference  to 
the  reliability  of  examination  grades  based  upon  short  samples 
will  be  presented  in  Chapter  IV.  It  is  possible  for  a  teacher  to 
make  examinations  more  comprehensive.  This  can  be  accomplish- 
ed in  part  by  exercising  more  care  in  the  preparation  of  the  ques- 
tions. The  "new  examination"  in  which  pupils  are  required  to  do 
little  or  no  writing  affords  one  means  for  covering  a  wide  range  of 
subject-matter  in  a  brief  period.  This  method  of  improving  ex- 
aminations will  be  discussed  in  Chapter  VI. 

The  final  point  to  be  made  with  reference  to  the  inaccuracy 
of  examination  marks  refers  to  the  distinction  between  a  "score" 
which  describes  a  pupil's  performance  on  the  examinafion  and 
a  "grade"  which  interprets  this  score  with  reference  to  a  norm. 
Failure  to  recognize  this  distinction  is  primarily  responsible  for 
too  high  grading  by  some  teachers  and  too  low  by  others.  Even 
the  same  teacher  is  likely  to  assign  "high  grades"  on  some  ex- 
aminations and  "low  grades"  on  others. 

In  order  to  understand  how  norms  (standards)  are  used  in 
connection  with  the  grading  of  examination  papers  it  is  necessary 
to  distinguish  between  "scores,"  or  measures,  and  "grades,"  or 
marks.  A  "score"  simply  describes  the  performance  which  has 
been  recorded  on  the  examination  paper.  For  example,  a  pupil 
may  answer  55  percent  of  the  questions  correctly.    In  this  case  55 


[11] 


is  his  "score."  If  a  certain  number  of  points  or  credits  had  been 
given  for  each  question  his  score  might  be  129,  or  91,  or  217.  A 
"grade"  interprets  this  description  with  reference  to  certain 
norms.  A  "grade"  indirectly  describes  a  pupil's  performance  on  an 
examination,  but  it  tells  also  whether  the  performance  is  to  be 
considered  as  above  or  below  passing;  whether  the  pupil  is  to  re- 
ceive the  highest  mark  or  the  lowest  mark  or  an  average  mark. 

It  is  customary  to  describe  the  quality  of  examination 
papers  in  terms  of  the  percent  of  questions  answered  correctly. 
For  example,  if  an  examination  includes  ten  questions  and  a 
pupil  answers  seven  of  them  correctly  and  an  eighth  one  partially 
right,  he  is  given  a  score  of  75  percent,  which  is  interpreted  to  mean 
that  in  the  judgment  of  the  examiner  he  has  answered  the  ques- 
tions 75  percent  correctly.  School  marks  or  "grades"  are  also 
frequently  expressed  in  terms  of  percents.  Sometimes  they  are 
expressed  in  terms  of  letters  or  other  symbols,  but  these  in  turn 
are  defined  in  terms  of  percents.  For  example,  the  grade  of  "A" 
may  be  defined  as  being  between  95  percent  and  100  percent. 
Since  both  "scores"  and  "grades"  are  generally  expressed  in 
terms  of  percents,  it  is  only  natural  that  the  two  have  been  con- 
fused and  that  "scores"  have  been  used  as  "grades." 

A  good  illustration  of  their  difference  came  to  the  writer 
recently.  An  examination  in  mathematics  was  given  to  nearly 
1000  freshmen  in  one  of  our  large  universities.  This  examination 
may  properly  be  described  as  "hard,"  considering  the  training 
which  the  students  had  received.  One  student  made  a  score  of 
100.  The  lowest  score  was  12.  The  average  was  approximately 
55.  From  the  standpoint  of  the  distribution  of  scores  this  was  a 
"good  examination."  If  it  had  been  easier,  so  that  any  consider- 
able number  of  pupils  received  scores  of  100  percent,  it  would  have 
been  unsatisfactory.  If  it  had  been  so  "hard"  that  a  considerable 
numberof  students  made  zero  scoresitwould  also  have  beendefect- 
ive.  In  both  cases  it  would  have  failed  to  differentiate  between 
some  students  who  were  not  equal  in  ability.  However,  obviously  an 
injustice  would  be  done  if  a  passing  mark  of  70  or  75  were  adopted 
and  all  pupils  having  scores  below  this  mark  were  given  a  grade 
of  failure.  The  passing  mark  for  this  particular  examination  should 
be  in  the  neighborhood  of  40.  If  the  "scores"  are  to  be  represented 
in  terms  of  "grades"  a  "score"  of  40  should  be  translated  into  a 
"grade"  of  70  or  whatever  passing  mark  has  been  adopted  by  the 
institution. 

[12] 


The  recognition  of  this  distinction  between  "scores"  and 
"grades"  enables  us  to  indicate  the  way  in  which  subjective  norms 
are  implied  in  "grades."  A  "grade"  is  not  a  pure  measure  or 
description  of  the  pupil's  performance.  It  is  rather  an  interpre- 
tation of  the  measure  of  his  performance  with  reference  to  certain 
norms.  When  no  distinction  is  made  and  "scores"  are  used  as 
"grades,"  pupils  will  receive  high  "grades"  if  the  examination  is 
"easy;"  and  low  ones  if  it  is  "hard."  Thus,  the  difficulty  of  the 
examination  is  one  factor  in  establishing  the  norms  with  reference 
to  which  the  "scores"  are  interpreted  when  they  are  used  as 
"grades."  Severe  marking  will  tend  to  set  high  norms.  Only  when 
the  examination  is  of  average  or  "standard"  difficulty  and  the 
marking  is  average  in  severity  do  "scores"  and  "grades"  become 
identical  in  magnitude.  Since  the  norms  are  established  by  the 
difficulty  of  the  examination  and  the  severity  of  the  scoring,  they 
must  be  subjective.  In  the  investigations  of  the  marking  of  ex- 
amination papers  it  was  shown  that  teachers  varied  widely  in 
their  judgments  concerning  the  worth  of  examination  papers. 
There  is  no  reason  to  expect  that  they  would  agree  more  closely 
in  estimating  the  difficulty  of  examinations.  Hence,  norms  which 
depend  upon  teachers'  estimates  of  the  questions  appropriate  for 
examinations  and  upon  their  marking  of  the  papers  must  be  con- 
sidered subjective.  It  is  possible  to  increase  greatly  the  objectivity 
of  these  norms  and  the  first  requirement  is  to  recognize  the  dis- 
tinction between  "scores"  and  "grades."  (See  page  38  for  a 
further  consideration  of  this  topic.) 

Summary  of  inaccuracy  of  examination  marks.  From  the 
preceding  discussion  examination  marks  are,  without  doubt, 
shown  to  be  far  from  accurate  measures  of  school  achievement. 
However,  it  does  not  necessarily  follow  that  the  errors  involved 
are  of  sufficient  magnitude  to  justify  the  abolishment  of  written 
examinations.  In  the  writer's  belief  the  greatest  benefit  will  come 
from  making  an  intelligent  inquiry  into  the  nature  of  these  errors 
and  from  taking  steps  to  reduce  them  to  the  lowest  magnitude. 

II.  Written  examinations  tend  to  encourage  undesirable 
mental  processes.  Many  critics  have  claimed  that  most  exami- 
nations, particularly  those  given  at  the  end  of  a  course,  tend  to 
encourage  "cramming."  The  assertion  is  made  that  many  stud- 
ents do  little  or  no  studying  until  near  the  close  of  the  term.  Then 
by  the  process  of  "cramming"  they  are  able  to  pass  the  final  ex- 

[13] 


amination  and  attain  a  relatively  high  standing  in  the  course. 
This  criticism  assumes  that  "cramming"  is  an  undesirable  mental 
process  and  that  final  examinations  are  responsible  for  its  occur- 
rence. The  undesirable  feature  is  the  neglect  of  study  throughout 
the  term.  This  is  not  due  to  the  fact  that  final  examinations  are 
given  but  that  undue  emphasis  is  placed  upon  them  and  that  the 
teacher  has  failed  to  check  up  on  the  student's  work  day  by  day 
throughout  the  term. 

One  of  the  points  which  may  be  made  in  favor  of  final  ex- 
aminations is  that  they  furnish  an  immediate  incentive  for  review 
and  organization  of  the  content  of  the  course.  The  writing  of  an 
examination  itself  may  be  an  important  part  of  the  student's 
learning.  This  is  particularly  true  in  the  case  of  questions  which 
require  reasoning  and  organization  of  information.  "There  is  no 
impression  without  expression,"  and  the  writing  of  a  three-hour 
examination  is  undoubtedly  an  intensive  form  of  expression. 
Hence,  one  is  justified  in  maintaining  that  written  examinations 
tend  more  to  encourage  desirable  mental  processes  than  undesir- 
able ones. 

III.  Passing  the  final  examination  an  undesirable  objective. 
The  assertion  has  been  made  that  when  a  final  examination  is 
required,  the  passing  of  it  tends  to  become  the  objective  for  which 
many  students  work.  When  this  occurs  it  is  due  not  to  the  fact 
that  the  final  examination  is  required  but  rather  to  the  undue 
emphasis  which  is  placed  upon  it  by  the  school.  If  an  examination 
consists  of  appropriate  questions  it  is  not  undesirable  to  have  the 
student  keep  it  in  mind  as  one  of  the  objectives  to  be  attained  by 
studying  the  subject-matter  of  the  course.  However,  as  we  shall 
show  later,  (see  page  25)  the  usual  practise  is  to  count  the  final  ex- 
amination grade  as  one-third  in  determining  a  student's  final 
standing.  In  many  schools  it  receives  less  weight.  When  the  final 
examination  counts  only  one-third  or  less  in  determining  a  stud- 
ent's final  standing  it  is  difficult  to  say  in  what  respect  it  forms  an 
important  educational  objective. 

IV.  Examinations  injurious  to  health  of  students.  Some 
critics  claim  that  written  examinations,  particularly  those  given 
at  the  end  of  a  course,  are  injurious  to  the  health  of  students, 
many  of  whom  make  very  strenuous  preparation  for  them.  The 
obvious  strain  which  accompanies  the  writing  of  answers  to  the 
questions  of  examinations  sometimes  lasting  two  or  three  hours 

[14] 


must  also  be  borne.  It  is  undoubtedly  true  that  both  the  prepar- 
ation and  the  writing  frequently  make  enormous  drains  on  the 
energies  of  students.  However,  no  careful  investigation  has  been 
conducted  of  the  actual  effect  upon  their  health.  To  one  who  ob- 
serves the  great  expenditures  of  time  and  energy  devoted  to  social 
and  athletic  activities,  it  is  difficult  to  believe  that  examinations 
are  in  general  more  injurious  to  the  health  of  students  than  many 
other  activities  in  which  they  are  permitted  and  even  encouraged 
to  engage.  Here  again  it  should  be  realized  that  this  criticism  is 
not  fundamentally  a  criticism  of  examinations,  but  rather  of 
setting  very  long  examinations  or  of  placing  extreme  emphasis 
upon  them  by  making  the  final  grade  of  the  course  depend  wholly 
or  very  largely  upon  the  examination  grade. 

V.  Time  devoted  by  teachers  to  written  examinations  not 
profitably  spent.  In  the  opinion  of  some  critics  the  time  given  to 
the  preparation  of  questions  and  particularly  to  the  marking  of 
examination  papers  might  be  more  profitably  employed.  Infor- 
mation concerning  the  time  actually  devoted  to  the  preparation 
and  the  administration  of  written  examinations  is  given  in  Chapter 
III.  However,  it  may  be  pointed  out  here  that  a  teacher  can  not 
attain  a  high  degree  of  efficiency  as  an  instructor  unless  he  checks 
up  the  work  of  his  students  in  order  to  assist  those  who  need 
supplementary  and  remedial  instruction.  Only  by  knowing  the 
extent  to  which  his  students  have  achieved  individually  and  col- 
lectively can  a  teacher  m^ke  his  instruction  fit  the  needs  of  his 
class.  Thus  considerable  time  must  be  given  to  measuring  the 
results  of  teaching.  This  is  an  indispensable  portion  of  the  teach- 
er's task.  It  is  only  when  a  teacher  devotes  an  undue  proportion 
of  his  time  to  the  preparation  and  administration  of  examinations 
that  such  work  tends  to  be  wasted.  Doubtless,  the  time  devoted  to 
written  examinations  might  in  many  cases  be  profitably  increased. 
Students  receiving  low  marks  should -have  their  answers  studied  in 
order  to  ascertain  in  what  ways  and  why  they  have  failed.  Such 
information  will  frequently  be  exceedingly  illuminating  to  the 
instructor,  and  aid  him  in  determining  his  own  shortcomings. 


[IS] 


CHAPTER  III 

PREPARATION  AND  ADMINISTRATION  OF 
EXAMINATIONS  IN  HIGH  SCHOOLS 

The  data  collected.  The  purpose  of  the  study  reported  in  this 
chapter  was  to  secure  information  concerning  the  present  practise 
in  the  preparation  and  administration  of  written  examinations  in 
high  schools.  A  questionnaire  was  mailed  in  the  fall  of  1922  to  254 
high-school  principals  in  Illinois  and  a  second  one  was  sent  to 
approximately  2900  high-school  teachers.^  One  hundred  and 
eighty-nine  replies  were  received  from  principals  and  1816  from 
teachers.  Of  the  latter  it  was  necessary  to  discard  eighty  so  that 
the  following  report  is  based  upon  returns  from  only  1736  high- 
school  teachers  who  are  distributed  as  follows: 

Commercial  Subjects 192  Modem  Languages 82 

Drawing  and  Art 26  Music 21 

English 342  Science 309 

Home  Economics 1 43  Shop  Work 58 

Latin 118  Social  Science 198 

Mathematics 247 

Representative  character  of  data  collected.  The  high  schools 
from  which  answers  to  the  questionnaire  were  received  ranged 
from  those  established  in  rural  communities  to  a  large  metro- 
politan high  school.  No  supplementary  investigation  was  made  to 
ascertain  the  extent  to  which  the  replies  were  representative  of 
conditions  in  Illinois  but  in  the  tabulations  there  was  no  indica- 
tion that  the  data  collected  were  not  representative  of  the  state. 
A  few  of  the  replies,  particularly  those  of  teachers,  suggest  that 
some  slight  misinterpretation  of  certain  of  the  questions  may  have 
been  made.  (See  page  23).  Such  cases,  however,  were  relatively 
rare  and  probably  did  not  affect  the  median  of  the  results. 

Extent  of  the  requirement  of  final  examinations  in  Illinois 
high  schools.  Evidence  of  the  subjectivity  of  the  marking  of  ex- 
amination papers,  together  with  other  adverse  criticisms  of  written 
examinations,  has  tended  to  cause  many  teachers  and  superin- 
tendents to  be  skeptical  of  their  value.    In  a  number  of  schools 

^These  questionnaires  are  reproduced  in  the  appendix  on  pages  66  and  68. 

[16] 


final  examinations  have  been  abolished  or  made  optional  with  the 
teachers  and  they  are  not  considered  essential  by  many  teachers. 
In  order  to  ascertain  the  present  practise  in  Illinois  the  high-school 
principals  were  asked,  "Do  you  require  your  teachers  to  give  final 
examinations?"  Only  twenty-one  principals  or  11  percent  stated 
that  final  examinations  were  not  required.  Thus  it  is  the  practise 
in  Illinois  high  schools  to  require  that  final  examinations  be  given. 
This,  however,  does  not  mean  that  all  students  must  take  them. 
Of  the  168  high  schools  in  which  final  examinations  are  required 
101  or  60  percent  reported  that  it  was  their  practise  to  exempt 
certain  students.  Scholarship,  that  is  making  a  grade  on  daily 
work  above  a  certain  average,  was  mentioned  by  all  of  these 
schools  as  one  of  the  conditions  on  which  exemption  was  based. 
Deportment  was  mentioned  by  52  percent  and  attendance  by  32 
percent  as  additional  conditions. 

No  information  was  secured  with  reference  to  the  explanation 
of  the  exemption  from  examinations  of  students  meeting  certain 
conditions  but  general  observation  has  indicated  that  two  reasons 
are  frequently  recognized.  The  first  is  that  promise  of  exemption 
from  the  final  examinations  operates  as  a  powerful  motive  to 
secure  a  high  quality  of  daily  work,  regular  attendance,  and  good 
deportment.  The  other  is  the  belief  held  by  many  teachers  that 
final  examinations  are  unnecessary  to  determine  a  student's  stand- 
ing in  a  course.  They  contend  that  the  average  of  a  student's 
daily  grades  should  be  taken  as  a  final  grade  for  the  course. 

There  is  no  doubt  that  the  promise  of  exemption  from  the 
final  examination  operates  as  a  powerful  motive  in  the  case  of 
many  students.  It  should,  however,  be  recognized  that  such  an 
incentive  is  artificial  and  therefore  open  to  criticism.  In  so  far  as 
possible  a  student  should  be  actuated  by  motives  which  sustain 
an  intrinsic  relation  to  the  subject-matter.  If  it  is  necessary  or 
advisable  that  the  final  examination  be  considered  as  a  motive, 
it  could  be  used  to  encourage  systematic  review  and  organization 
of  the  course.  This  should  constitute  a  very  important  phase  of 
studying.  Students  may,  of  course,  be  asked  by  their  teachers  to 
review  frequently  and  to  summarize  and  organize  the  work  at  the 
end  of  the  term,  but  they  cannot  be  convinced  easily  of  the 
necessity  of  such  work  if  it  receives  no  more  weight  in  determining 
their  final  grade  than  their  performances  during  an  equal  period 
of  time  elsewhere  in  the  course. 


[17] 


The  second  reason  is  a  valid  one  in  many  cases.  In  the  experi- 
ence of  most  teachers  the  mark  made  on  the  final  examination 
changes  the  standing  of  relatively  few  students.  Experienced 
teachers  can  under  favorable  conditions  estimate  with  consider- 
able accuracy  the  achievements  of  their  pupils.  If  the  class  is 
reasonably  small  and  if  the  teacher  has  used  methods  of  instruc- 
tion which  call  for  frequent  oral  and  written  performances  by  the 
students  and  has  kept  a  careful  record  of  these  performances 
throughout  the  term,  his  estimates  will  generally  be  relatively 
accurate  measures  of  the  achievements  of  the  students.  There  are, 
however,  certain  limitations  which  should  be  noted.  Teachers 
may  be  unduly  influenced  in  their  estimates  by  the  more  recent 
performances  of  their  students.  Unless  careful  records  have  been 
kept  throughout  the  term  inferior  work  at  the  beginning  tends  to 
be  overshadowed  by  good  or  excellent  work  during  the  closing 
weeks.  In  case  the  class  is  a  large  one  the  teacher  may  not  have 
an  adequate  opportunity  for  becoming  acquainted  with  all  of  its 
members. 

Teachers'  estimates  are  likely  to  be  materially  affected  by 
personal  characteristics  of  students;  one  with  a  pleasing  person- 
ality is  in  many  cases  rated  higher  than  one  who  is  unattractive. 
If  the  classwork  is  conducted  so  that  there  is  little  or  no  written 
performance  required,  teachers'  estimates  will  necessarily  be  based 
almost  wholly  on  the  oral  responses  given  during  the  class  period. 
Some  pupils  make  a  good  showing  in  class  when  the  recitation  is 
oral  but  are  at  a  decided  disadvantage  when  asked  to  record  their 
answers  in  writing.  Frequently  this  difficulty  is  encountered 
when  they  are  careless  in  their  thinking  and  do  not  have  clear 
ideas  to  express.  In  oral  recitation  they  are  able  to  make  a  fair 
showing  because  of  personal  characteristics  and  because  of  the 
stimulus  of  detailed  questioning  by  the  instructor.  Furthermore, 
in  a  class  discussion  a  bright  student  who  has  a  good  command  of 
language  may  easily  pick  up  ideas  from  other  members  of  the  class 
and  recall  ideas  from  his  general  experience  sufficient  to  make  a 
good  showing.  On  the  other  hand  there  are  students  who  express 
themselves  more  effectively  in  writing.  They  may  be  good  thinkers 
but  a  little  slow  in  their  mental  processes  and  not  clever  in  dis- 
cussion. Thus  there  are  cases  in  which  it  is  difficult  or  impossible 
for  a  teacher  to  estimate  accurately  the  real  achievements  of 
students  from  their  daily  work  alone.   The  final  examination  at  the 

[18] 


end  of  the  term  will  In  a  considerable  number  of  cases  furnish  ad- 
ditional information  which  is  needed  in  arriving  at  the  student's 
true  standing. 

The  final  examination  in  itself  provides  a  distinct  type  of  edu- 
cational opportunity  which  does  not  occur  elsewhere  in  the  course. 
Altho  the  writers  have  no  evidence  to  present  upon  this  point 
they  are  convinced  from  their  experience  with  college  students 
and  from  the  comments  of  a  number  who  have  been  exempted  from 
final  examinations  in  high  school  that  the  practise  deprives  stud- 
ents of  an  important  educational  opportunity.  Not  infrequently 
students  who  have  been  "excused  from  examinations"  in  high 
school  state  that  they  experienced  a  distinct  handicap  when  they 
entered  college.  If  final  examinations  can  be  justified  they  should 
be  required  of  all  students.  To  use  them  only  as  a  device  for  moti- 
vating the  work  of  the  term  destroys  much  of  their  value. 

Time  devoted  to  written  examinations.  Three  questions  were 
asked  relative  to  the  time  devoted  to  the  preparation  and  ad- 
ministration of  written  examinations.  The  replies  from  the  princi- 
pals indicated  that  the  most  frequent  practise  is  to  allow  ninety 
minutes  for  the  writing  of  a  final  examination.  This  is  the  time 
allowed  in  45  percent  of  the  schools  having  final  examinations. 
Fifteen  percent  allow  eighty  minutes  and  a  slightly  larger  percent 
one  hundred  and  twenty  minutes. 

The  teachers  were  asked  to  state  approximately  the  number 
of  minutes  which  they  use  "in  preparing  questions  for  a  final  ex- 
amination which  students  are  allowed  a  total  of  ninety  minutes  to 
answer."  The  median  time  which  varies  only  slightly  for  the  differ- 
ent subjects  is  approximately  fifty  minutes.  Individual  teachers 
in  the  same  subject  differ  widely  in  the  amount  of  time  which  they 
give  to  this  phase  of  their  work.  Two  teachers^  one  in  mathe- 
matics and  one  in  science,  stated  that  they  spent  more  than  six 
hours  in  the  preparation  of  a  set  of  final  examination  questions. 
In  each  subject  there  were  a  number  of  other  teachers  who  stated 
that  they  devoted  not  more  than  thirty  minutes  to  such  work. 
It  is  possible  that  some  teachers  failed  to  interpret  this  question 
correctly  but  doubtless  much  of  the  variation  is  due  to  differences 
in  the  practises  of  teachers  during  the  semester.  Some  probably 
make  a  memorandum  of  questions  as  they  occur  during  the  term 
and  use  this  list  as  a  basis  for  preparing  the  final  examination. 
Also  experience  is  a  contributing  factor.    Teachers  who  havebe- 

[19] 


come  very  familiar  with  the  subject  should  be  able  to  formulate 
questions  more  quickly  than  those  who  are  not  so  well  versed. 

The  teachers  were  asked  also  to  give  the  approximate  time 
which  they  used  in  "marking  the  papers  of  a  final  examination 
which  students  are  allowed  a  total  of  ninety  minutes  for  answer- 
ing." They  were  directed  to  base  their  estimates  upon  a  class  of 
twenty-five  students.  The  median  time  is  approximately  two  and 
one-half  hours.  The  variations  between  the  different  subjects  are 
not  large  when  the  differences  in  their  character  are  considered. 
The  greatest  number  of  hours  are  required  for  English  and  social 
science  and  the  least  for  drawing  and  art.  Here  also  there  were 
wide  variations  in  the  amount  of  time  reported  by  the  individual 
teachers.  A  total  of  twenty-five  teachers  in  which  all  subjects 
except  home  economics,  shop  work,  and  social  science  were  in- 
cluded, stated  that  they  devoted  not  more  than  thirty  minutes  to 
marking  a  set  of  papers  for  twenty-five  students.  On  the  other 
hand,  thirty-nine  teachers  stated  that  they  spent  480  minutes  or 
eight  hours  in  the  marking  of  a  single  set  of  papers. 

It  is  obvious  from  the  replies  received  that  some  teachers 
treat  this  phase  of  their  work  much  more  seriously  than  others  or 
that  they  employ  widely  different  methods.  Probably  some  correct 
all  errors  or  insert  references  which  will  enable  the  students  to 
correct  their  own  errors  when  the  papers  are  returned.  Others 
merely  check  the  errors  and  still  others  probably  do  not  attempt 
to  even  check  each  error  but  estimate  the  worth  of  the  paper  as  a 
whole.  The  question  concerning  the  amount  of  time  which  a 
teacher  is  justified  in  devoting  to  the  marking  of  a  set  of  examina- 
nation  papers  may  very  profitably  be  raised.  Final  examination 
papers  should  be  treated  seriously  and  there  should  be  an  earnest 
endeavor  on  the  part  of  the  teacher  to  estimate  as  accurately  as 
possible  the  grades  which  are  assigned  but  it  is  doubtful  if  the  ex- 
penditure of  as  much  as  twenty  minutes  per  paper  which  was  re- 
ported in  some  cases  could  be  justified.  The  median  practise  seems 
to  represent  a  more  reasonable  amount  of  time. 

Characteristics  noted  in  marking  examination  papers.  The 
principals  were  asked  to  state  whether  it  was  the  practise  in  their 
schools  for  teachers  to  subtract  from  a  pupil's  grade  for  (1)  poor 
writing,  (2)  poor  spelling,  (3)  poor  English.  Seventy-one  princi- 
pals or  42  percent  stated  that  teachers  were  accustomed  to  make 
deductions  for  poor  writing.   In  60  percent  of  the  schools  it  was  the 

[20] 


TABLE  I.    PERCENT  OF  TEACHERS  REPORTING  INTENTIONALLY 

LOWERING  A  STUDENT'S  GRADE  FOR  POOR  WRITING,  POOR 

SPELLING,  AND  POOR  ENGLISH 


Subject 

Poor  Writing 

Poor  Spelling 

Poor   English 

Ancient  Language 

31 
61 
65 
60 
37 
31 
31 
48 
35 
32 
37 

75 
74 
82 
96 
72 
48 
82 
60 
53 
77 
61 

80 

Commercial  Subjects 

72 

Drawing  and  Art 

67 

English 

98 

Home  Economics 

73 

Mathematics 

48 

Modern  Language 

74 

Music 

48 

Science 

Shop  and  Vocational 

56 

74 

Social  Science 

65 

practise  to  lower  a  student's  grade  for  misspelled  words  and  in  68 
percent  for  poor  English.  Fifteen  principals  or  9  percent  reported 
that  all  three  characteristics  were  recognized  only  in  the  marking 
of  papers  in  courses  in  English. 

The  teachers  were  asked  if  they  intentionally  lowered  a 
student's  grade  because  of  each  of  the  three  characteristics  men- 
tioned in  the  above  paragraph.  A  summary  of  their  replies  is  given 
in  Table  I,  which  indicates  considerable  variation  with  reference 
to  the  influence  of  poor  writing,  poor  spelling,  and  poor  English 
upon  examination  grades.  Since  writing,  spelling  and  English 
may  be  considered  essential  parts  of  courses  in  English  we  should 
naturally  expect  that  teachers  of  this  subject  would  intentionally 
lower  a  student's  grade  for  defects  in  any  of  these  characteristics. 
Outside  of  the  subject  of  English,  the  majority  of  teachers  do  not 
lower  a  grade  for  poor  writing  except  in  commercial  subjects,  and 
drawing  and  art.  With  the  exception  of  mathematics  deduction 
is  made  by  most  teachers  for  poor  spelling.  The  potency  of  poor 
English  in  determining  a  student's  grade  is  slightly  less  than  that 
of  spelling  in  a  number  of  subjects. 

The  handwriting,  spelling,  and  quality  of  English  which  a 
student  uses  in  writing  an  examination  should  be  recognized. 
It  does  not,  however,  follow  that  a  student's  standing  should  be 
intentionally  lowered  for  poor  handwriting,  poor  spelling,  and 
poor  English  in  school  subjects  other  than  English.  When  this  is 
done  his  grade  becomes  a  measure  of  these  abilities  as  well  as  of 
the  abilities  in  the  field  of  the  subject  in  which  the  examination  is 
given.     In  history,  for  example,  a  student's  grade  would  become  a 


[21] 


composite  measure  of  his  achievement  in  history,  the  legibility  of 
his  handwriting,  the  quality  of  his  spelling  and  the  use  of  grammati- 
cally correct  English.  As  a  result  both  the  teacher  and  the  student 
are  likely  to  be  confused  concerning  the  shortcomings  of  the  ex- 
amination paper.  A  better  procedure  would  be  to  keep  a  record  of 
the  errors  in  spelling,  poor  writing,  and  poor  English  and  when  it 
is  considered  desirable  a  separate  grade  may  be  given  covering 
these  three  characteristics.  Credit  for  a  course  may  be  withheld 
until  the  student  has  brought  his  handwriting,  spelling  and  Eng- 
lish up  to  a  satisfactory  standing. 

The  weighting  of  questions.  Sixty-four  percent  of  the  high 
school  principals  indicated  that  their  teachers  were  accustomed  to 
give  more  credit  for  correct  answers  to  difficult  questions  than  to 
easy  ones.  Approximately  four-fifths  of  the  teachers  replying  to 
the  questionnaire  stated  that  they  attempted  to  weight  examina- 
tion questions  on  the  basis  of  difficulty.  Thus  there  is  a  very' 
definite  effort  to  eliminate  the  errors  introduced  in  examination 
grades  by  the  unequal  difficulty  of  questions.    (See  page  10.) 

Recognition  of  rate  of  work.  Eighty-two  percent  of  the 
teachers  stated  that  they  were  accustomed  to  set  examinations 
short  enough  so  that  practically  all  students  could  answer  all  the 
questions.  Only  32  percent  noted  the  time  which  each  student 
spent  in  writing  his  examination  paper,  and  only  8  percent  said 
it  was  their  custom  to  set  examinations  long  enough  so  that  practi- 
cally no  student  would  have  time  to  answer  all  of  the  questions. 
Thus  it  is  clear  that  relatively  few  teachers  recognize  the  stud- 
ent's rate  of  work  in  determining  his  grade  on  an  examination. 

Incidentally  it  may  be  noted  that  when  examinations  are 
short  enough  so  that  practically  all  students  can  finish  a  great  deal 
of  time  is  wasted.  Individual  differences  exist  in  all  classes  and  it  is 
not  at  all  unusual  to  find  some  student  finishing  in  one-third  to 
one-half  of  the  time  which  others  devote  to  the  examination. 
Aside  from  the  waste  of  time  which  results  from  this  practise,  it  is 
likely  that  the  confusion  caused  by  the  leaving  of  those  pupils  who 
have  finished  tends  to  disturb  the  attention  of  those  who  are  still 
writing.  If  final  examinations  constitute  a  valuable  educational 
opportunity,  there  is  no  justification  for  wasting  time.  It  is  much 
better  to  set  an  examination  long  enough  so  that  practically  all 
students  will  be  occupied  for  the  entire  period. 


[22] 


TABLE  II.    PERCENT  OF  TEACHERS  GIVING  AFFIRMATIVE  ANSWERS 
TO  FOUR  QUESTIONS  RELATING  TO  THE  MARKING  OF  EXAMI- 
NATION PAPERS 


Subject 

Correct 
Answers 
Written 

Each  Ques, 
on  one 
paper 

One  Ques. 
on  all 
papers 

Each  paper 

as  a 

whole 

Ancient  Language 

9 

48 
40 
22 
19 
72 
15 
35 
27 
36 
18 

73 
82 
75 
76 
68 
75 
74 
80 
72 
75 
75 

24 
16 
25 
19 
24 
18 
23 
21 
27 
27 
22 

20 

Commercial  Subjects 

Drawing  and  Art 

31 

42 

English 

34 

Home  Economics 

38 

Mathematics 

24 

Modern  Language 

33 

Music 

42 

Science 

27 

Shop  and  Vocational 

Social  Science 

37 
40 

Method  of  marking  examination  papers.  Scientific  investi- 
gation has  revealed  that  the  reliability  of  examination  grades  can 
be  materially  increased  by  adopting  a  systematic  method  in  mark- 
ing papers.^  Among  the  procedures  recommended  are  the  writing 
out  of  correct  answers,  and  the  grading  of  one  question  on  all  of  the 
papers  before  taking  up  another  question.  In  order  to  ascertain 
the  practise  of  high-school  teachers  in  marking  examination  papers 
the  following  four  questions  were  included  in  the  questionnaire 
sent  to  them. 

1.  Before  starting  to  grade  a  set  of  examination  papers  do  you 
write  out  the  answers  which  you  consider  correct? 

2.  Do  you  usually  grade  all  the  answers  on  one  paper  before 
taking  up  those  of  another  paper? 

3.  Do  you  usually  grade  the  answers  to  one  question  on  all 
of  the  papers  before  taking  up  the  answers  to  a  second 
question? 

4.  Instead  of  marking  the  answers  to  each  question  separate- 
ly do  you  attempt  to  estimate  the  value  of  the  paper  as 
a  whole? 

The  percent  of  teachers  giving  affirmative  answers  to  these  ques- 
tions is  given  in  Table  II.  A  few  apparent  discrepancies  in  this 
table  are  due  to  the  fact  that  certain  teachers  did  not  answer 
all  the  questions.  Normally  we  should  expect  a  teacher  who  an- 
swered the  second  question  affirmatively  to  answer  the  third  one 
negatively.   This,  however,  did  not  always  happen. 


*Kelly,  F.  J.    "Teachers'  marks,"  Teachers  College  Contributions  to  Education, 
No.  66.    New  York:  Teachers  College,  1914,  83  p. 

[23] 


With  the  exception  of  mathematics,  it  is  not  the  custom  of 
teachers  to  write  out  the  answers  to  their  questions.  No  data  are 
at  hand  to  show  what  effect  this  has  upon  the  accuracy  of  the  ex- 
amination marks.  Experience  with  standardized  tests  would  indi- 
cate that  the  failure  to  write  out  correct  answers,  at  least  in  ab- 
breviated form,  would  operate  to  make  the  grading  of  examina- 
tion papers  less  accurate. 

About  three-fourths  of  the  teachers  are  accustomed  to  mark 
all  the  questions  on  one  paper  before  taking  up  another.  This  plan 
has  the  advantage  of  enabling  the  teacher  to  consider  a  pupil's 
performance  as  a  whole.  In  the  case  of  students  who  make  a  large 
number  of  errors  the  teacher  will  find  this  helpful  in  providing 
remedial  instruction.  It  has,  however,  been  proposed  that  the 
reliability  of  examination  grades  can  be  increased  by  marking  the 
answers  to  one  question  on  all  the  papers  before  taking  up  the 
answers  to  another  question. 

Directions  to  students  concerning  methods  of  work.  The 
high-school  teachers  were  asked  the  following  question,  "Do  you 
prepare  in  written  form  carefully  worded  directions  to  the  stud- 
ents regarding  the  procedure  they  are  to  follow  in  answering  the 
questions?  (These  directions  might  include  such  points  as,  order 
in  which  questions  are  to  be  answered,  length  of  answer,  arrange- 
ment of  work,  etc.)"  Only  35  percent  of  the  teachers  gave  an 
affirmative  answer.  It  is  possible  that  in  some  classes  there  is  a 
sufficiently  definite  understanding  concerning  the  methods  of 
work  to  be  followed  and  explicit  directions  are  unnecessary. 
However,  it  is  likely  that  in  many  cases  students  would  be  able  to 
give  more  truthful  evidence  of  their  ability  if  they  were  given  pre- 
cise directions  concerning  the  length  of  answer,  desired  arrange- 
ment of  work,  etc.  The  order  in  which  the  questions  are  to  be 
answered  is  a  point  which  should  be  stressed.  In  the  case  of 
questions  that  are  at  all  indefinite  or  general  there  should  be  speci- 
fications concerning  the  degree  of  elaborateness  which  is  expected 
in  the  answer. 

Recognition  of  a  standard  distribution  in  assigning  grades  to 
examination  papers.  The  teachers  were  asked  the  following  ques- 
tion, "In  assigning  grades  to  examination  papers  do  you  attempt 
to  have  their  distribution  conform  to  any  standard  form  such  as 
the  normal  distribution?"  Only  31  percent  of  the  teachers  gave  an 
affirmative  answer  to  this  question.    This  probably  means  that 

[24] 


relatively  few  teachers  have  recognized  the  distinction  between 
"scores"  and  "grades,"  (See  pages  11-13  for  an  explanation  of  this 
distinction.)  and  for  this  reason  are  neglecting  one  means  of  making 
their  grades  more  accurate  measures  of  school  achievement. 

Relation  of  examination  grades  to  final  grades.  The  princi- 
pals were  asked  if  they  advised  their  teachers  as  to  the  proportion 
of  the  final  mark  for  the  semester  which  should  be  based  upon  the 
final  examination.  Only  eleven  or  7  percent  replied  negatively. 
Of  those  who  gave  advice  on  this  matter  95  percent  made  a  definite 
ruling.  The  most  frequently  mentioned  proportions  allotted  the 
final  examination  are  25,  30,  33^,  and  40  percent.  In  4  percent  of 
the  schools  the  examination  counts  for  one-half  in  determining  a 
student's  final  grade,  in  1.3  percent  for  only  one-tenth  of  the  final 
grade.  The  teachers  were  also  asked  this  same  question.  The 
replies  varied  from  10  percent  to  50  percent.  Except  in  science  and 
shop  work,  the  median  practise  is  to  estimate  the  final  examina- 
tion mark  as  one-third  in  determining  a  pupil's  final  grade.  A 
considerable  number  of  teachers  indicated  that  they  gave  not 
more  than  one-fourth  or  one-fifth  value  to  the  final  examination. 

Summary.  The  typical  practise  with  reference  to  final  ex- 
aminations in  Illinois  high  schools  may  be  summarized  as  follows: 

1.  Final  examinations  are  required  of  students  and  exempt- 
ions are  made  largely  on  the  basis  of  scholarship. 

2.  Students  are  allowed  ninety  minutes  for  writing  a  final 
examination.  Teachers  spend  slightly  less  than  one  hour  in  pre- 
paring examination  questions  and  from  two  to  to  three  hours  in 
grading  a  set  of  papers  for  twenty-five  students. 

3.  With  the  exception  of  mathematics,  the  majority  of  teach- 
ers lower  a  student's  grade  for  spelling,  and  with  the  exception  of 
mathematics  and  music  the  majority  lower  it  for  poor  English. 
Poor  writing  is  not  a  potent  factor  except  in  English,  commercial 
subjects,  and  drawing  and  art. 

4.  About  three-fourths  of  the  teachers  attempt  to  weight  the 
questions  on  the  basis  of  difficulty. 

5.  The  majority  of  the  teachers  do  not  consider  rate  of  work 
in  estimating  the  grade  assigned  the  final  examination  paper. 

6.  The  majority  of  teachers  do  not  write  out  the  answers  to 
the  questions  preparatory  to  the  marking  of  papers.  The  general 
practise  is  to  mark  all  answers  on  one  paper  before  taking  up  the 
next. 

7.  About  one  teacher  in  three  writes  out  directions  with 
reference  to  the  procedure  which  the  students  shall  use  in  answer- 
ing the  questions. 

[25] 


8.  About  one  teacher  in  three  tries  to  have  his  grades  con- 
form to  a  standard  distribution. 

9.  The  proportion  of  the  final  mark  for  the  semester  which  is 
based  upon  the  final  examination  grade  varies  from  10  to  50  per- 
cent. The  median  practise  is  33}^  percent.  The  majority  of  the 
principals  make  a  definite  ruling  regarding  the  value  placed  upon 
the  final  examination. 


[26] 


CHAPTER  IV 

THE  CONSTANT  AND  VARIABLE  ERRORS  IN 
EXAMINATION  GRADES 

Constant  and  variable  errors  of  measurement.^  Two  types 
of  errors  are  encountered  in  educational  measurement.  The  pres- 
ence of  variable  errors  is  indicated  when  a  test  is  given  twice  to 
the  same  group  of  pupils.  The  two  average  scores  of  the  group 
may  be  the  same  but  this  will  not  be  true  for  individual  pupils. 
A  few  pupils  will  make  the  same  or  approximately  the  same  score 
on  the  two  trials.  Others  will  make  higher  scores  on  the  second 
trial  than  on  the  first,  while  still  others  will  make  lower  scores  on 
the  second  trial  than  on  the  first.  If  we  assume  that  the  average  of 
the  two  scores  obtained  represents  an  approximately  true  measure 
of  a  pupil's  achievement  then  the  differences  between  the  first  set 
of  scores  and  the  corresponding  average  scores  would  be  the  vari- 
able errors  of  the  measures  resulting  from  the  first  application  of 
the  test.  Some  of  these  differences  approximate  zero.  Some  of 
them  are  positive  and  about  an  equal  number  negative.  Another 
set  of  variable  errors  would  be  obtained  by  using  the  scores  se- 
cured from  the  second  application  of  the  test.  In  the  case  of  a 
number  of  pupils  the  variable  errors  for  the  first  application  of  the 
test  will  not  be  the  same  as  those  for  the  second  application.  Thus, 
as  the  name  implies,  variable  errors  change  in  magnitude  from 
pupil  to  pupil  within  a  group  and  also  for  the  same  pupil  in  a 
series  of  measurements  of  the  same  achievements. 

A  constant  error  is  the  same  for  all  members  of  a  group. 
Such  an  error  occurs  in  teachers'  marks  where  there  is  a  tendency 
to  grade  too  high  or  too  low.  It  is  found  in  the  case  of  standard- 
ized educational  tests  when  mistakes  occur  in  the  time  allowed  or 
when  other  departures  are  made  from  standard  testing  conditions. 
A  constant  error  may  be  either  positive  or  negative  and  it  is  gen- 
erally different  for  different  tests. 

^For  a  more  detailed  discussion  of  the  nature  and  magnitude  of  the  constant  and 
variable  errors  of  educational  measurement,  see  Monroe,  Walter  S.  "The  constant 
and  variable  errors  of  educational  measurements."  University  of  Illinois  Bulletin, 
Vol.  21,  No.  10,  Bureau  of  Educational  Research  Bulletin  No.  15.  Urbana:  University 
of  Illinois,  1923.    30  p. 

[27] 


\ 


These  two  types  of  errors  usually  occur  in  combination,  that 
is,  a  given  measurement  may  and  frequently  does  involve  both  a 
constant  error  and  a  variable  error.  The  actual  error  is  a  combi- 
nation of  these  two.  However,  in  studying  the  accuracy  of  edu- 
cational measurementsit  is  helpful  to  distinguish  between  the  two 
types  and  to  consider  each  separately.  The  usual  method  used 
for  calculating  an  index  of  the  magnitude  of  the  variable  errors 
does  not  give  any  indication  of  the  magnitude  of  the  constant 
error.  Also  the  method  commonly  used  for  determining  the  pres- 
ence and  probable  magnitude  of  constant  errors  does  not  yield 
an  index  of  the  variable  errors.  Furthermore,  different  methods 
are  required  for  decreasing  the  two  types  of  errors  in  educational 
measurements. 

Methods  of  describing  the  magnitude  of  the  variable  errors 
of  measurement  yielded  by  standardized  educational  tests.    In 

describing  the  magnitude  of  variable  errors  in  the  measures  yielded 
by  standardized  educational  tests,  the  usual  method  is  to  have  the 
test  given  twice  to  a  typical  group  of  pupils  under  as  nearly  the 
same  conditions  as  possible.  The  coefficient  of  correlation  be- 
tween the  two  sets  of  measures  is  taken  as  the  index  of  the  magni- 
tude of  the  variable  errors.  Usually  there  will  be  a  constant  error 
in  one  and  sometimes  in  both  of  the  sets  of  measures  but  the  sta- 
tistical procedure  used  is  such  that  this  error  does  not  affect  in  any 
way  the  coefficient  of  correlation  secured.  This  coefficient  of  cor- 
relation is  commonly  spoken  of  as  the  coefficient  of  reliability. 
A  coefficient  of  1.00  would  mean  that  the  variable  errors  were 
zero. 

Available  data  with  reference  to  the  magnitude  of  errors  of 
examination  grades  and  standardized  test  scores  not  comparable. 

Investigations  of  the  Starch-Elliott  type  have  proven  that  ex- 
amination grades  involve  errors  but  the  method  which  they  em- 
ployed is  different  from  that  used  in  studying  the  errors  in  the 
scores  yielded  by  standardized  educational  tests.  Starch  and 
Elliott  confined  their  efforts  to  a  study  of  the  subjectivity  of  the 
marking  of  a  single  examination  paper.  Except  in  the  use  of 
quality  scales,  as  in  handwriting  and  English  Composition,  the 
scoring  of  standardized  educational  tests  has  been  made  highly  ob- 
jective. Hence,  there  has  been  little  need  for  studying  the  sub- 
jectivity of  the  marking  of  test  papers.    On  the  other  hand,  there 


[28] 


has  not  been,  so  far  as  the  writers  are  aware,  any  reported  attempt 
to  apply  to  written  examinations  the  method  commonly  used  in 
studying  the  reliability  of  standardized  educational  tests.  Hence, 
comparisons  to  show  the  relative  reliability  of  the  two  types  of 
measuring  instruments  cannot  as  yet  be  made. 

For  this  reason  in  the  present  investigation  it  has  seemed 
worth  while  to  apply  to  written  examinations  the  same  method 
which  is  commonly  used  in  studying  the  reliability  of  educational 
tests.  Certain  modifications  are  of  course  necessary.  These  will 
be  noted  in  the  following  paragraphs.  The  investigation  pertains 
primarily  to  the  variable  errors  Involved  in  examination  grades. 
Incidentally  some  light  will  be  thrown  upon  the  magnitude  of  con- 
stant errors. 

Methods  employed  in  the  present  investigation  of  the  relia- 
bility of  written  examinations.  The  essential  feature  of  the  meth- 
ods employed  In  the  present  investigation  is  securing  two  Inde- 
pendent examination  grades  for  each  pupil  for  the  same  units  of 
work.  This  requires  that  two  examinations  be  given  to  each  of  the 
groups  of  students  from  which  data  were  secured.  Two  methods 
were  used.  These  are  described  In  the  following  directions  which 
were  sent  to  those  cooperating  In  this  Investigation. 

Method  I 

Two  sets  of  examination  questions  are  to  be  prepared  by  a 
single  person,  or  two  or  more  persons  working  together.  Each 
of  the  two  lists  should  contain  the  same  number  of  questions. 
There  should  be  a  distinct  effort  to  make  the  two  lists  approxi- 
mately equal  In  difficulty  and  as  nearly  as  possible  similar  in  re- 
spect to  the  type  of  questions. 

After  the  two  lists  of  questions  have  been  made  both  should 
be  given  by  each  teacher  to  all  of  her  pupils  under  as  nearly  the 
same  conditions  as  possible.  If  not  given  on  the  same  day,  the  two 
examinations  should  be  given  within  a  period  of  one  week.  For 
example,  if  two  sets  of  examination  questions  in  seventh  grade 
geography  have  been  prepared,  both  sets  of  questions  should  be 
given  by  each  seventh  grade  teacher  to  all  of  her  pupils. 

Each  teacher  is  to  mark  both  sets  of  examination  papers  for 
her  pupils.  In  marking  these  papers  the  teacher  should  indicate 
the  credit  given  for  each  question  and  write  the  total  grade  plainly 
upon  the  examination  paper.  When  two  or  more  teachers  have 
given  the  same  examinations  it  is  not  necessary  that  they  confer 
In  regard  to  the  marking  of  the  papers.  If  this  Is  done  a  memor- 
andum regarding  the  procedure  should  be  attached  to  the  exam- 
ination papers. 

[29] 


This  method  may  be  followed  by  a  single  teacher  who  has 
two  or  more  sections  of  a  given  subject.  Both  examinations  should 
be  given  to  all  sections  taught  by  this  teacher.  This  method  of 
studying  the  reliability  of  written  examinations  can  be  applied 
to  any  school  subject.  The  Bureau  of  Educational  Research  is 
most  interested  in  having  it  applied  to  arithmetic,  history,  geogra- 
phy, and  language  in  the  elementary  school  and  to  history,  math- 
ematics, English,  and  science  in  the  high  school. 

Method  II 

Two  sets  of  examination  questions  for  the  same  subject  are 
to  be  prepared  by  two  teachers  working  independently,  each 
teacher  preparing  a  set.  There  is  no  requirement  concerning  the 
length  or  the  difficulty  of  the  two  sets  of  examination  questions 
except  that  both  should  cover  the  same  amount  of  work.  The 
teachers  who  prepare  the  questions  should  not  confer  concerning 
either  the  kind  or  the  number  of  questions  asked. 

After  the  questions  have  been  prepared,  both  sets  are  to  be 
given  by  each  teacher  to  all  of  her  pupils.  If  not  given  on  the 
same  day,  the  two  examinations  should  be  given  within  a  period  of 
one  week. 

After  the  examinations  have  been  given  each  teacher  will 
grade  all  of  the  papers  written  upon  the  questions  that  she  pre- 
pared. This  will  mean  that  she  will  grade  a  set  of  papers  for  her 
own  pupils  and  also  a  set  for  the  pupils  of  the  other  teacher. 
There  should  be  no  conferring  between  the  teachers  in  regard  to  the 
method  of  scoring.  In  marking  these  papers  the  teacher  should  in- 
dicate the  credit  given  for  each  question  and  write  the  total  grade 
plainly  upon  the  examination  papers. 

The  data  collected.  Through  the  city  superintendents  and 
high-school  principals  a  general  invitation  was  extended  to  school 
systems  in  Illinois  to  participate  in  this  investigation  at  the  close 
of  the  second  semester  1921-22  and  also  at  the  close  of  the  first 
semester  1922-23.  No  instructions  other  than  those  just  noted 
were  given  to  those  who  cooperated.  It  should,  therefore,  be 
borne  in  mind  that  the  data  collected  are  for  written  examinations 
as  they  are  usually  given  and  not  for  special  types  of  examinations 
or  for  unusual  methods  in  the  administration  or  the  grading  of  the 
test  papers.  The  reliability  of  examination  grades  could  probably 
have  been  increased  if  certain  directions  had  been  formulated  in 
regard  to  the  marking  of  the  examination  papers  but  the  purpose 
of  the  investigation  was  to  determine  the  reliability  of  typical 
written  examinations  administered  in  the  usual  way. 

Returns  were  secured  from  seventy-two  groups  of  children 
but  it  was  necessary  to  discard  the  data  for  six  groups  because 

[30] 


instructions  liad  not  been  followed.  The  examinations  given  to  the 
sixty-six  groups  were  all  of  the  traditional  type.  The  papers  were 
marked  by  the  teachers  on  the  scale  of  100  percent,  and  were  then 
sent  to  the  Bureau  of  Educational  Research.  The  coefficients  of 
reliability  reported  in  this  chapter  were  calculated  under  the  di- 
rection of  the  writers. 

Coefficients  of  reliability  of  examination  grades.  The  coeffi- 
cients of  reliability  of  written  examinations  for  the  sixty-six 
groups  of  students  are  summarized  in  Table  III.  This  table  also 
shows  the  number  of  students  in  each  class,  the  number  of  ques- 
tions in  each  examination  and  the  method  followed  in  giving  the 
examination.  The  reliability  coefficients  have  been  grouped  by 
subjects  and  have  been  arranged  in  descending  order  of  magni- 
tude. For  those  entries  marked  with  an  asterisk  (*)  in  the  column 
headed  "Method,"  one  of  the  examinations  was  given  by  the  prin- 
cipal or  some  other  person  not  actually  teaching  a  class  in  the  sub- 
ject at  that  time.  However,  this  person  was  considered  competent 
to  be  in  charge  of  the  examination.  The  total  distribution  of  re- 
liability coefficients  is  given  in  Table  IV. 

Two  of  the  coefficients  of  reliability  are  negative.  The  high- 
est is  .95.  It  is  interesting  to  note  that  the  coefficients  given  for 
history  are,  on  the  average,  higher  than  those  obtained  for  arith- 
metic. The  most  reliable  examinations  given  were  in  algebra. 
With  the  exception  of  history,  arithmetic,  and  algebra,  the  num- 
ber of  groups  is  so  small  that  comparisons  can  not  have  much 
significance.  The  median  coefficient  of  reliability  .65  may  be 
used  as  a  general  index  of  the  reliability  of  written  examinations. 

The  coefficients  of  reliability  of  standardized  educational 
tests.  McCall'  has  stated  that  the  "range  of  self-correlation  for 
many  standardized  tests  is  about  .5  to  about  .9."  The  writer's 
experience  has  indicated  a  somewhat  greater  range.  In  Table  V 
the  reliability  of  a  number  of  standardized  educational  tests  is 
given.  Those  for  the  silent  reading  tests  by  Brown,  Starch  and 
Courtis  are  taken  from  a  recent  bulletin^  by  the  writer.  The  range 
in  this  table  is  from  .19  to  .92. 


^McCall,  W.  A.  How  to  Measure  in  Education.  New  York:  The  Macmillan 
Company,  1922,  p.  396. 

'Monroe,  Walter  S.  "A  critical  study  of  certain  silent  reading  tests."  University 
of  Illinois  Bulletin,  Vol.  19,  No.  22,  Bureau  of  Educational  Research  Bulletin  No.  8. 
Urbana:  University  of  Illinois,  1922,  p.33-34. 

[31] 


TABLE  III.    COEFFICIENT  OF  RELIABILITY  FOR  WRITTEN  EXAMINA- 
TIONS SET  BY  TEACHERS 


Class 
Number 

No.  of 
Pupils 

No.  of 
Questions 

Coefficient 
Correlation 

Method 

64  (Arithmetic) 

21 
35 
24 
38 
64 
37 
38 
88 
41 
33 
72 
17 
22 
55 
73 
27 
56 
21 
43 
27 

51 
20 
23 
37 
36 
52 
45 
54 

33 

54 
53 

74 

15 
43 
27 
37 
21 
52 

10 
7  and  8 
10 
10 
10 
5 

10 
10 

5  and  10 

10 

6 

10 

7  and  10 

6 

10 

5 

5 

6  and  10 

10 

8  and  10 

10 

30  and  19 

5  and  7 

10  and  6 

10 

6 

15 

6 

5 
5 
5 

5 

3 

5 
5 

7  and  45 
6   and   7 
5   and   8 

.76 
.74 
.73 
.71 
.69 
.67 
.64 
.64 
.61 
.60 
.56 
.48 
.48 
.47 
.47 
.33 
.30 
.29 
.06 
—.18 

.92 
.91 
.88 
.82 
.81 
.78 
.73 
.61 

.68 
.62 
.57 

.19 

.78 
.53 
.53 
.50 
.47 
.41 

II 

58             "           

II 

43            "           

II 

63            "          

II 

61            "          

II 

2            "          

1 

62            "          

I 

1            "          

I 

60            "          

II 

65           "          

II 

4            "          

I 

71            "          

* 

44            "          

II 

3            "          

I 

66            "          

II 

23           "          

I 

32           "          

II 

59           "          

I 

45           "          

II 

42           "          

II 

5     (Algebra)    

I 

72            "          

* 

50            "          

II 

34            "          

II 

57            "          

II 

6            "          

35            "          

II 

31            "          

II 

7    (Language) 

9            "          



"8         "        ..; 



10  (Literature)  . . . .- 

I 

18      (English)    

I 

12            "           

II 

11             "           

I 

54            "          

II 

53            "          

II 

13            "          

II 

[32] 


TABLE  III.    (Continued)    COEFFICIENT  OF  RELIABILITY  FOR  WRITTEN 
EXAMINATIONS  SET  BY  TEACHERS 


Class 
Number 

No.  of 
Pupils 

No.  of 
Questions 

Coefficient 
Correlation 

Method 

20      (History)    

14 
28 
19 
43 
19 
53 
32 
28 
64 
24 
30 

29 
29 
47 
21 
23 
26 

63 

31 
30 
50 

33 

42 
10 
46 

18 

23 

16 

5 

5 

5 

5 

9 

5 
8  and  10 
5  and  7 

5 

10 
5  and  10 

10 

5  and  10 

5  and  10 

5 
10  and  8 
10  and  5 

5 

8 

2 

6  and  8 

5 

5 

8 

4  and  5 

5 

7  and  8 
16  and  10 

.95 

.85 
.78 
.76 
.75 
.75 
.67 
.66 
.63 
.57 
.55 

.66 
.66 
.62 
.43 
.32 
—  .11 

.39 

.89 
.82 
.68 

.87 

.75 
.68 
.34 

.79 

.83 

.53 

15            "           

I 

23            "          

I 

36            "          

II 

56            "          

* 

67            "          

II 

41            "          

II 

40            "          

II 

14            "          

I 

48            "          

II 

49            "          

II 

39  (Geosraphv) 

II 

46            "          

II 

47            "          

II 

16            "          

I 

68            "          

* 

38            "          

II 

17       (Civics)     

I 

37       (Latin)      

19            "          

II 
I 

51            "          

II 

21      (Spelling)    

I 

52    (Geometry) 

II 

70            "          

* 

22            "          



24     (Spanish)    

I 

33     (German)    

I 

69   (Commerce) 

* 

[33] 


TABLE  IV.    SUMMARY  DISTRIBUTION  OF  COEFFICIENTS  OF  RELIA- 
BILITY FOR  WRITTEN  EXAMINATIONS 


Size  of  Coefficient 

Frequency 

of  Correlation 

.95 

1 

.00 

2 

.85 

4 

.80 

4 

.75 

9 

.70 

4 

.65 

9 

.60 

8 

.55 

4 

•50 

4 

•                  .45 

5 

.40 

2 

.35 

1 

.30 

4 

.25 

1 

.20 

0 

.15 

1 

.10 

0 

.5 

1 

0 

0 

—  .5 

0 

—.10 

0 

—  .15 

1 

—.20 

1 

Total 

.66 

Median 

.65 

From  certain  unpublished  studies  by  the  writer  the  follow- 
ing information  has  been  obtained.  The  Courtis  Standard  Re- 
search Test,  Series  B,  Forms  1  and  2  were  given  to  pupils  as  fol- 
lows: Grade  V,  89;  Grade  VI,  81 ;  Grade  VII,  52;  and  Grade  VIII, 
38.  The  thirty-two  coefficients  of  reliability  ranged  from  .409 
to  .904  with  the  median  at  .665.  Forms  1  and  3  were  given  to  a 
slightly  larger  group  in  each  of  the  four  grades.  The  thirty-two 
coefficients  of  correlation  between  the  two  sets  of  scores  for  this 
administration  of  Series  B  ranged  from  .528  to  .963  with  the 
median  at  .704.  The  Woody  Arithmetic  Scales,  Series  A,  were 
given  to  several  groups  of  pupils.  Two  scores  were  secured  by 
using  alternate  items  of  each  of  the  scales  and  applying  Brown's 
formula.*  The  twelve  coefficients  of  reliability  computed  in  this 
way  ranged  from  .91  to  .46  with  the  average  at  .66.    Forms  1  and 


*  2rh      In  this  formula  r^  is  the  correlation  between  two  scores  which  this 

1+rh    test  yields.      One  is  based  upon  reproduction  and  the  other  upon 
answers  to  questions. 

[34] 


TABLE  V.    RELIABILITY  COEFFICIENTS  OF  STANDARDIZED  EDUCA- 
TIONAL TESTS 


Test 

Illinois  General  Intelligence  Scale* 

Courtis  Standard  Research  Tests,  Series  Bt 

Brown  Silent  Reading  Test — Rate 

Courtis  Silent  Reading  Test,  No.  2 — Rate 

Otis  Group  Intelligence  Scale§ 

Monroe  Standardized  Silent  Reading  Test  Revised* — Rate 

Courtis  Silent  Reading  Test,  No.  2 — Comprehension — No.  Quest 

Starch  Silent  Reading  Test — Comprehension — Words 

Monroe  General  Survey  Scale  in  Arithmetic* 

Monroe  Standardized  Silent  Reading  Test  Revised* — Comprehension. 

Monroe  Standardized  Silent  Reading  Test  Revised* — Rate 

Monroe  Standardized  Silent  Reading  Test  Revised* — Comprehension. 

Starch  Silent  Reading  Test — Comprehension — Ideas 

Indiana  Attainment  Scale,  No.  IT 

Starch  Silent  Reading  Test — Rate 

Pressey  Primer  ScaleT 

Courtis  Silent  Reading  Test,  No.  2 — Comprehension — Index 

Pressey  First  Grade  Vocabulary  ScaleT 

Brown  Silent  Reading  Test — Comprehension — Quantity' 

Pressey  Primer  ScaleT 

Brown  Silent  Reading  Test — Comprehension — Quality 


Coefficient 


.92 
.87 
.86 
.85 
.84 
.84 
.80 
.77 
.76 
.76 
.75 
.72 
.72 
.66 
.62 
.59 
.58 
.37 
.36 
.33 
.19 


*Monroe,  Walter  S.  "The  Illinois  Examination."  University  of  Illinois  Bulletin,  Vol.  19,  No. 
9,  Bureau  of  Educational  Research  Bulletin  No.  6.    Urbana :  University  of  Illinois,   1921,  p.  47. 

tPressey,  L.  W.  "A  Group  Scale  of  Intelligence  for  Use  in  the  First  Three  Grades:  its  validity 
and  reliability,"  Journal  of  Educational  Research,    1  :285-94,  April,    1920. 

ttUnpublished  data  of  the  Bureau  of  Educational   Research,  University  of  Illinois. 

§Colvin,  S.  S.  "Some  recent  results  obtained  from  the  Otis  Group  Intelligence  Scale,"  Journal 
of  Educational  Research,   3:1-12,  January,   1921. 

2  of  Monroe's  Standardized  Reasoning  Test  in  Arithmetic  were 
given  to  pupils  as  follows:  Grade  V,  36;  Grade  VI,  92;  Grade  VII, 
76;  Grade  VIII,  81.  The  coefficients  of  reliability  for  correct 
principle  were  as  follows:  .530,  .630,  .645,  and  .723;  for  correct 
answer  they  were  .518,  .528,  .576,  and  .707.  Using  Brown's 
formula  the  coefficients  of  reliability  for  Gray's  Silent  Reading 
Tests  were  computed  for  thirty  grade  groups.  These  coefficients 
ranged  from  .55  to  .85  with  the  median  at  .67.  The  number  of 
pupils  per  group  was  less  than  100  in  only  five  cases.  For  several 
grade  groups  reliability  coefficients  were  secured  for  Monroe's 
Standardized  Silent  Reading  Tests  which  ranged  from  .222  to  .907 
with  an  average  of  .669. 

Haggerty  has  computed  the  reliability  for  both  Sigma  1  and 
Sigma  3  of  his  Reading  Examination  by  having  the  same  test  re- 
peated. In  the  case  of  Sigma  1  the  interval  between  the  two  appli- 
cations of  the  test  was  six  weeks.  For  200  children  in  Grades  I  to 
III  inclusive  the  coefficient  of  reliabilitv  .84  was  obtained.    In  the 


[35] 


case  of  Sigma  3  the  interval  between  the  two  applications  was  only 
two  days.  For  126  pupils  from  Grades  V  to  VIII,  inclusive,  the 
coefficient  of  reliability  was  found  to  be  .885.  For  the  sentence 
test  alone  the  reliability  coefficient  was  .769  and  for  the  paragraph 
test,  .806.  For  Thorndike's  Scale  Alpha  for  the  Understanding  of 
Sentences,  McCall  has  reported  a  coefficient  of  reliability  of  .37. 
This  was  obtained  by  using  a  test  similar  to  Alpha  but  not  con- 
sidered a  duplicate  form.  Gates^  reported  reliability  coefficients 
for  Thorndike-McCall  Reading  Scale  which  ranged  from  .25  to  .72. 
All  of  these  were  for  pupils  belonging  to  a  single  grade.  For  the 
Burgess  Picture  Supplement  Scale  the  author  has  given  coeffi- 
cients of  reliability  ranging  from  .62  to  .88  for  grade  groups  from 
the  second  to  sixth  grades  inclusive.  In  each  case  the  number  of 
pupils  was  relatively  small.  Gates  gave  coefficients  of  .62,  .59  and 
.66  for  three  grade  groups. 

For  the  Otis  Self-Administering  Test  of  Mental  Ability  the 
author  has  reported  an  average  reliability  coefficient  of  .921  for 
the  higher  examination  and  of  .948  for  the  intermediate  examina- 
tion. Presumably  these  coefficients  are  based  on  the  scores  se- 
cured from  pupils  for  a  sequence  of  several  grades.  For  the 
separate  tests  of  the  Stanford  Achievement  Test  the  authors  re- 
ported coefficients  of  reliability  based  upon  separate  grade  groups 
which  ranged  from  .75  to  .96.  When  the  composite  score  of  all  the 
tests  was  used  the  reliability  coefficient  was  .98. 

The  relative  reliability  of  written  examinations  and  stand- 
ardized educational  tests.  The  data  which  have  just  been  sub- 
mitted indicate  that  the  difference  between  the  reliability  of  the 
two  types  of  instruments  is  not  as  great  as  is  commonly  believed. 
The  median  of  the  reliability  coefficient  for  written  examinations 
given  in  Table  IV  is  .65.  There  are  many  reliability  coefficients 
for  standardized  tests  in  Table  V  which  are  less  than  this.  Further- 
more, the  additional  citations  of  coefficients  of  correlation  in  the 
above  paragraphs  indicate  that  for  a  number  of  standardized  edu- 
cational tests  which  have  been  very  widely  used  the  median  of  the 
reliability  coefficients  for  grade  groups  is  in  the  neighborhood  of 
.65.  Thus  the  conclusion  seems  justified  that  altho  some  of  our 
more  elaborate  standardized  tests,  such  as  the  Stanford  Achieve- 


*Gates,  Arthur  I.    "An  experimental  statistical  study  of  reading  tests,"  Journal 
of  Educational  Psychology,  12:379,  October,  1921. 

136} 


/ 


ment  Test,  the  Illinois  General  Intelligence  Scale,  and  the  Otis 
Self-Administering  Test  of  Mental  Ability,  may  be  expected  to 
yield  measures  whose  reliability  is  greatly  in  excess  of  that  of 
typical  written  examinations,  many  widely  used  standardized 
educational  tests  yield  measures  which  possess  about  the  same 
degree  of  reliability  as  the  grades  obtained  from  written  exam- 
inations prepared  by  teachers  and  other  school  officials.  It 
should  be  noted  that  reliability  refers  only  to  the  variable  errors 
of  measurement.  The  constant  errors  as  we  shall  show,  (p.  40) 
are  likely  to  be  very  much  larger  in  examination  grades  than  in 
the  scores  yielded  by  standardized  educational  tests.  It  should 
also  be  noted  that  the  time  required  to  give  many  of  the  stand- 
ardized tests  is  much  less  than  that  devoted  to  a  typical  written 
examination. 

The  absolute  reliability  of  examination  grades.  The  state- 
ment that  the  reliability  of  a  typical  examination  is  equivalent  to 
that  of  many  standardized  tests  and  only  slightly  less  than  that  of 
a  number  of  others  still  leaves  a  doubt  with  reference  to  the  abso- 
lute reliability.  For  practical  purposes  the  reliability  coefficient 
of  .65  needs  to  be  interpreted  in  terms  of  the  variable  errors  of 
measurement  to  be  expected.  The  correlation  tables  for  eight 
groups  having  a  reliability  coefficient  of  approximately  .65  were 
taken  and  the  scores  translated  into  a  five  point  system  of  school 
grades.  It  is  assumed  that  these  classes  were  typical  and  the  high- 
est scores  were  translated  into  a  mark  of  "A,"  the  lowest  into  a 
mark  of  "E."  This  was  done  in  an  arbitrary  way  but  the  results 
indicate  roughly  one  meaning  which  may  be  attached  to  a  re- 
liability coefficient  of  .65.  It  was  found  that  in  40  percent  of  the 
cases  the  students  received  the  same  grade  in  the  two  examina- 
tions. In  an  additional  42  percent  the  grade  which  they  received 
on  the  first  examination  was  only  one  point  higher  or  lower  than 
that  received  on  the  second.  For  example,  if  a  student  in  this 
group  made  a  "D"  on  one  examination,  he  made  an  "E"  or  "C" 
on  the  other.  The  two  grades  received  by  the  remaining  18 
percent  differed  by  two  points  or  more. 

Conditions  tending  to  produce  variable  errors  of  measure- 
ment in  examination  grades.  Several  sets  of  examination  papers 
were  examined  in  order  to  ascertain  the  conditions  which  tended 
to  produce  the  lowest  coefficients  of  reliability  and  hence  the 
largest  variable  errors  of  measurement.    The  most  potent  cause 

[37] 


appeared  to  be  that  the  two  teachers  recognized  widely  different 
educational  objectives  in  making  out  the  two  sets  of  examination 
questions.  This  seemed  to  be  the  case  in  Group  42,  arithmetic, 
for  which  the  coefficient  of  correlation  was  —.18.  In  Group  22, 
geometry,  there  was  a  difference  in  the  general  plan  of  the  exami- 
nations; one  teacher  permitted  the  students  to  choose  one  of  two 
questions  in  part  of  the  examination  while  the  other  required  that 
all  questions  be  answered.  This  difference  in  the  plan  of  the  ex- 
amination appeared  to  increase  the  variable  errors  of  measure- 
ment. There  was  also  a  difference  in  the  educational  objectives 
recognized  in  that  one  teacher  placed  much  more  emphasis  upon 
the  practical  application  of  geometry  than  the  other. 

Another  cause  which  operated  to  lower  the  degree  of  correla- 
tion and  hence  to  increase  the  magnitude  of  the  variable  error  was 
the  adherence  to  different  standards  of  excellence  by  the  teachers 
who  graded  the  papers.  For  example,  in  Group  45,  arithmetic, 
one  teacher  considered  only  the  final  answer  to  the  exercise;  if  that 
was  right  the  student  received  full  credit — if  wrong,  no  credit  was 
given.  ■  The  other  teacher  gave  credit  for  correct  principle.  The 
coefficient  of  reliability  for  this  group  was  .06. 

It  was  noticed  that  in  general  pupils  made  higher  grades  on 
the  tests  set  by  their  own  teacher  than  on  those  set  by  another 
person.  This  appeared  to  be  true  even  when  distinct  differences 
could  not  be  identified  either  in  the  educational  objectives  or  in 
the  methods  of  grading  of  the  two  teachers.  In  Group  32  for  which 
a  reliability  coefficient  of  .30  was  obtained  when  the  grades  made 
on  the  first  examination  were  correlated  with  those  made  on  the 
second  examination,  a  second  coefficient  was  calculated  by  com- 
paring the  student's  grade  made  on  the  examination  prepared  by 
his  own  teacher  with  that  set  by  another  teacher.  This  procedure 
gave  a  coefficient  of  correlation  of  .40.  When  the  two  classes  were 
taken  separately  coefficients  of  .57  and  .44  were  obtained.  These 
data  tend  to  supplement  the  evidence  already  cited  that  differ- 
ences in  the  content  of  the  examination  and  in  the  plan  of  marking 
are  potent  factors  in  producing  the  variable  errors  of  measurement. 

The  magnitude  of  constant  errors  in  examination  grades. 
It  is  probable  that  most  of  the  teachers  marking  the  examination 
papers  did  not  recognize  the  distinction  between  "scores"  and 
"grades"^  and  that  the  marks  placed  upon  the  papers  were  con- 

*See  page  11  for  a  statement  of  this  distinction. 

[38] 


TABLE  VI. 


DISTRIBUTION  OF  DIFFERENCES  BETWEEN  AVERAGES 
OF  EXAMINATION  GRADES 


Difference 

Frequency 

50 

1 

32 

1 

29 

1 

27 

1 

22 

1 

21 

1 

20 

2 

18 

3 

16 

1 

15 

1 

14 

2 

13 

2 

12 

1 

10 

2 

9 

1 

8 

4 

7 

3 

6 

6 

5 

4 

4 

6 

3 

5 

2 

6 

1 

8 

0 

3 

Total 

66 

Median 

6.2 

sidered  as  "grades."  In  several  instances  the  "grades"  made  on 
one  examination  were  on  the  average  much  higher  than  those 
made  on  the  other.  If  "scores"  were  used  as  "grades,"  any  differ- 
ences between  the  averages  of  the  two  sets  of  measures  indicate 
the  presence  of  constant  errors.  In  order  to  secure  an  index  of 
their  magnitude  the  differences  were  calculated  for  the  sixty-six 
groups  to  which  two  examinations  were  given.  These  are  assem- 
bled in  Table  VI.  For  three  of  these  groups  the  difference  between 
the  averages  of  the  two  sets  of  "grades"  was  zero;  for  eight  other 
groups  it  was  one.  At  the  other  extreme  we  find  a  difference  of  50 
in  the  case  of  one  group.    The  median  difference  is  6.2. 

It  should  be  noted  that  the  differences  between  the  averages 
of  two  sets  of  examination  grades  are  not  constant  errors.  They 
are  merely  indicative  of  the  presence  of  constant  errors.  If  one 
examination  was  easy  and  the  other  hard  the  difference  would  be 
the  sum  of  a  positive  error  and  a  negative  error.  If  both  examina- 
tions were  hard  the  difference  would  be  smaller  than  the  constant 
error  in  either  average.    The  large  differences  shown  in  Table  VI 

[39] 


are  probably  caused  by  the  combination  of  an  easy  examination 
with  a  difficult  one.  This  was  very  obviously  true  in  the  case  of 
the  one  difference  of  50.  Furthermore,  in  interpreting  Table  VI  it 
should  be  remembered  that  possibly  some  of  the  teachers  recog- 
nized the  distinction  between  "scores"  and  "grades,"  and  the 
marks  would  have  been  appropriately  adjusted  before  being  used 
as  "grades." 

So  far  as  it  was  possible  to  ascertain  from  an  analysis  of  the 
examination  papers  the  large  differences  are  due  to  two  causes — 
differences  in  the  difficulty  of  the  two  sets  of  examination  ques- 
tions and  in  the  severity  of  the  grading.  For  example  one  of  the 
examinations  which  produced  a  difference  of  40  consisted  of  seven 
questions  of  which  the  pupils  were  permitted  to  answer  any  five. 
These  questions  were  relatively  easy.  In  the  other  examination, 
there  were  ten  questions  and  the  pupils  were  required  to  answer 
all  of  them.  Very  few  were  able  to  complete  this  second  examina- 
tion in  the  time  allowed  and  the  teacher  appears  to  have  counted 
the  unfinished  exercises  as  failures.  Nine  out  of  twenty-two  child- 
ren in  the  second  group  made  zero  on  the  examination.  In  this 
way  a  very  large  constant  error  was  introduced  but  the  coefficient 
of  reliability  for  this  group  was  .48. 

Relative  magnitude  of  constant  errors  in  examination  grades 
and  in  standardized  test  scores.  In  another  place^  the  writer  has 
discussed  the  magnitude  of  the  constant  errors  in  educational  tests. 
In  cases  where  there  has  been  coaching  for  tests,  intentional  or  not, 
or  disregard  for  standard  directions,  large  constant  errors  have 
been  introduced.  In  one  extreme  instance  a  constant  error  of  over 
three  and  a  half  years  occurred  in  the  mental  age  scores  of  a  group  of 
children.  In  general,  however,  because  of  the  standard  directions 
for  administering  the  tests  and  scoring  the  papers,  of  the  objectiv- 
ity of  the  marking,  and  of  the  norms  for  interpreting  test  scores, 
the  constant  errors  in  standardized  tests  are  very  much  smaller, 
and  are  likely  always  to  be  smaller  than  those  found  in  examina- 
tions given  by  teachers.  However,  some  reduction  in  the  magni- 
tude of  the  constant  errors  in  examination  scores  will  result  when 
the  use  of  either  very  easy  or  very  difficult  sets  of  questions  is 
avoided  and  when    a  conservative  plan  of  marking  is  followed. 


TMonroe,  Walter  S.  "The  constant  and  variable  errors  of  educational  measure- 
ments." University  of  Illinois  Bulletin,  Vol.  21,  No.  10,  Bureau  of  Educational  Re- 
search Bulletin  No.  15.    Urbana:  University  of  Illinois,  1923,  p.19-20. 

[40] 


Explanation  of  the  apparent  contradiction  between  the  re- 
sults of  this  investigation  and  previous  studies  of  examination 
grades.  The  results  of  this  investigation  have  caused  the  writers 
to  revise  their  estimate  of  the  accuracy  of  examination  grades. 
The  findings  indicate  that  the  errors  are  much  less  than  they  ap- 
peared to  be  from  evidence  resulting  from  investigations  of  the 
Starch-Elliott  type.  One  naturally  asks  the  question,  "Why  this 
apparent  contradiction?"  Starch  and  Elliott  obtained  similar  re- 
sults for  three  different  examination  papers  and  numerous  other 
investigators  have  corroborated  their  findings.  The  mass  of  evi- 
dence accumulated  is  so  extensive  and  uniform  in  character  that 
one  would  naturally  be  inclined  to  accept  the  conclusions  indicated 
in  preference  to  the  apparent  contradictory  results  of  the  present 
investigation.  However,  a  careful  analysis  of  the  procedures  re- 
veals that  the  results  are  not  necessarily  contradictory.  The 
method  followed  by  Starch  and  Elliott  combines  both  constant 
errors  and  variable  errors.  The  "grades"  assigned  to  the  exami- 
nation paper  in  geometry  were  influenced  both  by  the  subjectivity 
of  the  marking  and  by  the  tendency  of  some  teachers  to  grade  high 
and  of  others  to  grade  low.  The  present  investigation  has  separat- 
ed the  variable  errors  from  the  constant.  It  has  also  shown  that 
the  examination  scores  have  in  some  cases  involved  relatively 
large  constant  errors.  The  extreme  differences  between  the  grades 
assigned  to  the  same  paper  reported  by  Starch  and  Elliott  (see 
page  9)  are  easily  explained  when  it  is  understood  that  they  repre- 
sent the  combination  of  variable  errors  and  constant  errors. 
Especially  is  this  true  when  we  realize  that  the  constant  errors 
would  likely  be  larger  for  teachers  of  different  schools  as  in  their 
investigation  than  for  teachers  in  the  same  school  as  in  the  present 
investigation. 

Conclusion  with  reference  to  relative  accuracy  of  examination 
grades  and  scores  yielded  by  standardized  tests.  As  already 
indicated  the  writers  believe  that  the  data  presented  in  this 
chapter  show  that  examination  grades  are  more  accurate  meas- 
ures of  achievement  than  many  persons  have  considered  them  to 
be.  Standardized  tests  yield  scores  involving  errors,  both  con- 
stant and  variable,  but  in  the  case  of  our  best  standardized  tests 
these  errors  are  distinctly  less  than  the  corresponding  errors  in  ex- 
amination grades.  Furthermore,  measurement  by  means  of 
standardized  tests  usually  requires  much  less  time  than  is  com- 

[41] 


monly  devoted  to  written  examinations.  This  conclusion  refers 
to  written  examinations  of  the  traditional  type  and  admin- 
istered under  typical  conditions.  It  is  likely  that  written  examina- 
tions and  their  administration  may  be  improved  so  that  the 
difference  in  the  accuracy  of  examination  grades  and  test  scores 
will  become  much  less  than  at  present.^ 


^Theconditionsof  standardized  tests  would  have  been  more  closely  approximated 
if  both  sets  of  examination  questions  had  been  prepared  by  the  same  person  and  marked 
by  different  persons.  If  this  had  been  done  it  is  reasonable  to  expect  that  the  coeffi- 
cients of  reliability  would  have  been  somewhat  higher  and  the  differences  in  the  aver- 
ages of  the  two  sets  of  scores  smaller. 

[42] 


CHAPTER  V 
THE  CONTENT  OF  WRITTEN  EXAMINATIONS 


The  data  collected.  In  response  to  an  invitation  sent  to 
superintendents  and  high-school  principals  in  Illinois  sets  of  ex- 
aminations were  received  from  fifty-six  schools  for  the  first  semes- 
ter and  from  fifty  schools  for  the  second  semester  of  the  school 
year  1921-22.  A  range  of  approximately  sixty  subjects  was  repre- 
sented. It  seemed  desirable  to  restrict  this  analysis  of  sets  of 
questions  to  the  thirteen  subjects  listed  in  Table  VII.  The  num- 
ber of  sets  of  questions  and  also  the  total  number  of  questions  are 
given  in  this  table. 

Classification  of  questions  according  to  type.  After  consider- 
able experimentation  a  list  of  fifty  types  of  questions  as  given  be- 
low was  formulated. 


Aims  \  — 

Analysis 

Cause  (give) 

Classification 

Comparison 

Completion 

Conjugation 

Construction   (a  figure,  study 

or  statement) 
Construction  (give  the) 
Contrast  (general) 
Contrast  (specific  basis) 
Correction 
Criticism 

Decision  (choice  or  preference) 
Declension 
Definition 

Description   (characterization) 
Diagram  (illustrate  by) 
Discussion 
Effect  (give  the) 
Evaluation 

Example  (illustrate  by) 
Expansion 

Explanation  (tell  why  or  how) 
Facts  (definite  number) 
Facts  (indefinite  number) 
Factoring 


How  many   (tell) 

Law  (give  the) 

Mathematical  operations  of  addition, 
subtraction,  multiplication,  and  divi- 
sion 

Method 

Outline 

Parsing 

Proof 

Punctuation  (capitalize  and 
correct  sentences) 

Recall 

Reduction  to  lowest  terms 

Relationships  (give  the) 

Rule 

Scanning 

Simplification 

Source 

Substitution  (values  for  letters) 

Summary 

Solving  for  unknown  quantity 

Syllabus 

Translation  (foreign  language  to 
English) 

Translation   (English  to  foreign 
language) 

Use   (give  the) 

Where  (tell) 


[43] 


TABLE  VII.    NUMBER  OF  QUESTIONS  AND  SETS  OF  QUESTIONS 

EXAMINED 


Subject 

English  I 

English  II 

English  III 

Algebra  I 

Plane  Geometry 

Latin  I 

Latin  II 

Physics 

General  Science 

Civics 

American  History 

Domestic  Science 

Domestic  Art 

Total 


Sets 


901 


Questions 


80 

721 

83 

694 

79 

721 

80 

731 

80 

636 

81 

683 

76 

539 

76 

795 

62 

789 

59 

560 

62 

550 

42 

392 

41 

368 

7621 


All  questions  for  the  thirteen  subjects  mentioned  in  Table  VII 
were  classified  under  some  one  of  these  types.  This  classification 
was  made  by  Mr.  Souders  with  the  assistance  of  a  single  clerk 
working  under  his  immediate  direction.  Altho  any  classification 
of  this  kind  is  necessarily  subjective,  a  relatively  high  degree  of 
uniformity  has,  we  believe,  been  secured. 

Summary  of  classification.  Twenty-six  of  the  fifty  types  of 
questions  were  represented  in  six  or  more  of  the  thirteen  subjects. 
The  relative  frequency  of  each  is  given  in  Table  VIII.  This  classi- 
fication of  examination  questions  shows  a  high  frequency  of  cer- 
tain types  and  very  little  or  no  use  of  a  number  of  other  types. 
If  we  omit  Latin,  Algebra,  and  Plane  Geometry  in  which  the  na- 
ture of  the  subject-matter  restricts  the  kind  of  question  asked, 
we  find  that  32  percent  of  all  the  questions  require  "explanation." 
The  next  most  frequent  type  used,  21  percent,  calls  for  a  "definite 
number  of  facts." 

Frequently  all  questions  are  considered  as  belonging  to  one  of 
two  groups,  "thought  questions"  or  "memory  questions."  Such  a 
definite  classification  is  not,  however,  always  possible.  The 
character  of  the  mental  process  involved  in  answering  depends 
upon  the  person  replying  as  well  as  upon  the  form  of  the  question 
asked.  Those  questions  calling  for  definite  facts  are  almost  cer- 
tain to  be  based  upon  memory;  on  the  other  hand,  those  requiring 
classification,   evaluation,   contrast,   etc.    are   likely    to   demand 


[44] 


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[45] 


thought  on  the  part  of  most  students.  If,  however,  such  classifi- 
cations or  evaluations  have  been  made  in  a  previous  class  exercise 
some  students  may  easily  remember  the  answers  and,  in  such  a 
case,  a  thought  question  for  one  student  becomes  a  memory  ques- 
tion for  another.  For  the  purpose  of  this  study  Types  10,  20,  22, 
25,  and  26  have  been  designated  as  probable  memory  questions, 
the  remaining  types  as  probable  thought  questions.  The  percent 
of  each  group  is  given  in  the  last  two  lines  of  Table  VIII.  These 
percents  can  be  considered  as  only  a  rough  indication  of  the  re- 
lative frequency  of  these  two  very  general  divisions. 

In  her  investigation  of  "the  question  as  a  measure  of  effi- 
ciency in  instruction,"  Dr.  Stevens^  attempted  to  determine 
the  relative  number  of  thought  questions  and  memory  questions 
asked  by  teachers  in  a  single  class  period.  The  percents  of  memory 
questions  for  history,  English  and  science  were  83,  55,  and  67 
respectively.  This  relative  frequency  is  much  larger  than  indi- 
cated in  Table  VIII.  The  difference  may  be  due  to  the  fact  that 
in  the  present  investigation  only  written  examination  questions 
were  considered,  but  it  is  altogether  likely  that  it  is  indicative  of  a 
real  change  in  the  type  of  questions  which  teachers  commonly  ask 
of  their  students. 

Relation  of  questions  to  educational  objectives.  The  ques- 
tions which  teachers  ask  during  class  periods  constitute  a  concrete 
expression  of  the  educational  objectives  which  they  are  day  by 
day  setting  for  their  students.  The  questions  of  the  final  examina- 
tions should,  therefore,  be  representative  of  the  types  of  education- 
al objectives  set  in  the  different  school  subjects.^  The  emphasis 
upon  memory  and  some  of  the  simpler  types  suggests  a  need  for 
a  modification  in  emphasis  in  most  of  the  school  subjects. 

Quality  of  examination  questions.  Altho  the  writers  have  no 
objective  evidence  to  present  in  regard  to  the  quality  of  examina- 
tion questions,  those  submitted  for  this  study  were  in  general 
considered  good.  Catch  questions  or  those  stated  so  that  they 
would  not  be  understood  easily  by  students  were  very  rare.  Many 
questions  were  stated  so  that  the  grading  of  the  answers  was  ob- 
jective and  would  indicate  that  their  form  had  been  influenced  by 


'Stevens,  Romiett.  "The  question  as  a  measure  of  efficiency  in  instruction." 
Teachers  College  Contributions  to  Education,  No.  48.  New  York:  Teachers  College, 
Columbia  University,  1912. 

^See  page  55  for  a  further  discussion  of  objectives  in  school  subjects. 

[46] 


the  exercises  of  standardized  tests.  This  was  especially  true  of 
those  examinations  having  questions  of  the  true-false  or  recogni- 
tion type.  In  the  judgment  of  the  writers  the  criticism  that  teach- 
ers are  inclined  to  ask  misleading  or  catch  questions  is  not  a  valid 
one  in  the  case  of  the  examinations  studied  in  this  investigation. 


[47] 


CHAPTER  VI 
THE  IMPROVEMENT  OF  WRITTEN  EXAMINATIONS 

Altho  we  now  have  a  number  of  standardized  tests  which  are 
superior  to  written  examinations,  and  we  have  reason  to  believe 
that  they  will  be  used  even  more  extensively  than  at  present,  there 
is  need  to  give  attention  to  the  improvement  of  written  examina- 
tions. It  does  not  appear  likely  that  standardized  tests  will  ever 
replace  written  examinations.  The  latter  type  of  measuring  in- 
strument will  probably  continue  to  be  the  most  frequently  used 
means  of  measuring  the  achievements  of  school  children. 

Written  examinations  may  be  improved  by  correcting  the 
faults  which  have  been  noted  in  the  preceding  chapter.  In  this 
chapter  we  shall  consider  four  important  improvements:  (1) 
Reduction  of  constant  errors;  (2)  Reduction  of  variable  errors; 
(3)  Securing  a  greater  agreement  of  the  content  of  examinations 
with  recognized  educational  objectives;  (4)  Simplification  of  the 
administration  of  written  examinations. 

There  is  some  overlapping  between  these  improvements. 
For  example,  the  magnitude  of  errors  in  measurement,  particularly 
variable  errors  of  measurement,  will  be  reduced  by  securing  a 
greater  agreement  between  the  content  of  the  examination  and 
recognized  educational  objectives.  The  devices  for  simplifying  the 
administration  of  examinations  also  tend  to  make  the  results  more 
accurate. 

Causes  of  constant  errors  in  examination  grades.  The  fun- 
damental cause  of  constant  errors  in  examination  grades,  i.e., 
"high  grades"  or  "low  grades,"  is  the  failure  to  recognize  the  dis- 
tinction between  "scores"  and  "grades."  (See  page  11.)  A 
pupil's  grade  tells  his  standing  with  reference  to  a  norm,  i.e.,  the 
passing  mark.  When  no  distinction  is  made  between  "scores" 
and  "grades"  this  norm  is  subjective.  Altho  the  passing  mark  may 
be  defined  numerically  as  70  percent  or  85  percent  it  is  fixed  in  the 
case  of  a  particular  examination  by  the  difficulty  of  the  questions 
and  by  the  severity  of  the  marking  of  the  papers.  Pupils  will  re- 
ceive "high  grades"  when  the  examination  is  easy  or  the  plan  of 

[48] 


marking  is  generous.  They  will  receive  "low  grades"  when  the 
examination  is  hard  and  a  severe  plan  of  marking  is  followed. 
If  the  teacher  makes  no  distinction  between  "scores"  and  "grades" 
he  sets  the  norm  for  a  particular  examination  when  he  makes  out 
the  questions  and  decides  upon  the  plan  of  marking.  He  implicitly 
expresses  the  opinion  that  the  pupil  whose  achievements  are  barely 
"passing"  will  make  a  grade  of  70,  or  the  passing  mark  adopted. 
He  also  implies  that  the  pupil  whose  achievements  are  exception- 
ally high  will  make  a  high  grade,  i.e.,  a  grade  of  95  or  between  95 
and  100.    Such  expressions  are  merely  subjective. 

Since  the  failure  to  recognize  the  distinction  between  "scores" 
and  "grades"  is  the  cause  of  constant  errors  the  plan  for  improve- 
ment is  obvious.  The  papers  should  be  marked  in  terms  of 
"scores."  These  may  be  on  the  scale  of  100  but  this  is  not  essen- 
tial. In  fact  it  will  probably  assist  a  teacher  in  keeping  the  dis- 
tinction in  mind  if  the  scores  are  not  on  the  scale  of  100.  After  the 
papers  have  been  marked  the  "scores"  should  be  translated  into 
"grades"  by  comparison  with  a  norm  in  which  the  subjective  ele- 
ments are  reduced  to  a  minimum. 

A  standard  average  grade  used  as  a  norm.  The  simplest  ob- 
jective^ norm  is  a  standard  average  grade.  This  may  be  set 
arbitrarily  but  a  more  rational  procedure  would  be  to  take  the 
average  of  the  grades  given  in  a  school  on  a  particular  subject 
during  a  period  of  several  years. 

The  standard  average  grade  defines  the  grade  into  which  the 
average  score  of  a  typical  class  should  be  translated.  For  ex- 
ample, if  the  standard  average  grade  is  85  and  the  average  score  in 
a  particular  class  is  57  the  grade  corresponding  to  this  score  would 
be  85.  In  case  the  class  is  made  up  of  poor  students  the  average 
grade  of  the  class  should  be  below  the  standard  average  grade. 
If  the  class  is  unusually  bright  their  average  grade  should  be 
higher  than  the  standard  average.  The  translation  of  the  average 
score  into  the  appropriate  corresponding  grade  furnishes  a  basis 
for  the  translation  of  the  other  scores  of  the  group. 

The  procedure  just  outlined  is  necessarily  crude.  It  is  par- 
tially subjective  because  the  determination  of  the  general  status  of 


^The  adjective  "objective"  is  not  intended  to  indicate  perfect  objectivity  or  even 
as  high  a  degree  of  objectivity  as  we  have  in  the  case  of  many  standardized  tests.  As 
used  here  it  means  that  the  norm  is  distinctly  less  subjective  than  the  norm  commonly 
implied  in  the  usual  examination. 

[49] 


the  class  is  left  to  the  teacher.  However,  the  teacher  may  use 
previous  school  records  or  the  measures  obtained  from  a  stand- 
ardized test  to  assist  him  in  arriving  at  a  partially  objective  es- 
timate of  the  general  status  of  the  class.  The  use  of  a  standard 
distribution  instead  of  merely  a  standard  average  grade  represents 
a  more  systematic  procedure. 

1.  Decreasing  the  magnitude  of  constant  errors  by  means  of 
a  standard  distribution  of  grades.  For  several  years  a  number  of 
educators  have  been  urging  that  teachers  make  the  distributions 
of  their  grades  conform  to  a  standard  shape,  i.e.,  that  a  specified 
percent  of  the  members  of  a  typical  class  be  given  a  grade  of  A, 
another  specified  percent  a  grade  of  E,  and  so  on  for  each  of  the 
marks  adopted  by  the  school.^  A  number  of  distributions  have 
been  recommended.  For  a  five  point  system  of  grades  several 
authors  have  recommended  the  following  distribution,  7,  24,  38, 
24,  7.  Other  distributions  which  have  been  advocated  are  7,  18, 
50,  18,  7  and  5,  15,  60,  15,  5. 

The  essential  feature  of  the  plan  is  a  specification  of  the  per- 
cent of  the  students  of  a  given  group  who  are  to  receive  each  mark 
rather  than  the  particular  form  of  distribution  used.  There  is 
much  evidence  which  indicates  that  the  distribution  of  achieve- 
ments of  an  unselected  group  of  students  approximates  the  normal 
probability  curve. ^  If  we  assume  that  true  measures  of  the 
achievements  of  an  unselected  group  of  100  or  more  are  distributed 
normally  this  adjustment  does  not  fix  the  percent  who  are  to  re- 
ceive each  grade.  The  normal  probability  curve  may  be  divided 
in  many  ways,  for  example,  it  is  possible  to  divide  the  curve  so  that 
there  would  be  50  percent  of  A's,  20  percent  of  B's,  10  percent  of 
C's,  10  percent  of  D's,  and  10  percent  of  E's.  In  such  a  distribu- 
tion a  grade  of  A  would  be  given  to  all  students  above  the  average 
of  the  class.  An  appropriate  meaning  could  be  stated  also  for  each 
of  the  grades.  A  distribution  which  is  symmetrical  has  certain 
advantages  and  one  of  those  mentioned  in  the  preceding  para- 
graph is  to  be  preferred.  The  particular  standard  distribution  to 
be  used  is  a  matter  of  policy  which  each  school  should  determine. 
Some  argue  that  different  standard  distributions  be  adopted  for 


-If  grades  are  expressed  in  percents  the  corresponding  intervals  such  as  95  to  100, 
90  to  94,  etc.  would  be  used  instead  of  A,  B,  C,  etc. 

The  normal  probability  curve  is  bell  shaped  and  Is  symmetrical  with  the  average 
or  median  as  a  center. 

[SO] 


the  different  years  of  the  high  school,  some  advocate  different 
standard  distributions  for  different  school  subjects.  It  should  be 
noted,  however,  that  there  are  certain  advantages  in  uniformity. 
It  would  be  desirable  for  all  high  schools,  particularly  those  in  a 
given  state,  to  agree  upon  a  common  standard  distribution  and  to 
use  this  for  all  subjects.  Grades  assigned  in  different  schools  can 
have  a  common  meaning  only  when  they  conform  to  the  same 
standard  distribution. 

The  proposal  that  teachers  make  the  distributions  of  their 
grades  conform  to  a  standard  shape  has  met  with  much  criticism. 
As  in  any  controversy  there  have  been  extremists  on  both  sides 
and  many  of  those  participating  have  given  evidence  that  they 
failed  to  understand  clearly  the  nature  of  the  proposal  of  its  es- 
sential features.  Among  the  advocates  of  the  use  of  a  standard 
distribution  are  those  who  have  insisted  that  the  normal  probabil- 
ity curve  explicitly  defines  the  students  who  must  receive  A's,  who 
must  receive  B's,  etc.  Cases  have  been  reported  of  instructors 
who  frankly  admitted  that  a  certain  student  deserved  to  receive  an 
A  but  that  they  had  used  up  all  the  A's  which  the  distribution  al- 
lowed, and  that,  therefore,  the  student  must  be  satisfied  with  a  B. 
One  hears  also  of  instructors  who  announce  at  the  beginning  of  a 
course  that  a  certain  number  of  the  class  must  fail.  It  is  rumored 
that  in  some  of  these  instances  the  students  enrolled  have  hired 
certain  other  students  who  were  indifferent  to  their  scholastic 
standing  to  enter  the  course  in  order  to  provide  the  requisite  num- 
ber of  failures.  The  opponents  of  the  use  of  a  standard  distribu- 
tion have  contended  that  there  was  no  a  priori  reason  why  any 
student  should  fail  and  that  always  the  quality  of  the  student's 
work  should  determine  his  scholastic  standing.  Furthermore,  they 
have  pointed  out  that  in  any  group  of  students  brought  together 
for  instructional  purposes  it  is  extremely  unlikely  that  the  distri- 
bution of  achievement  would  approximate  at  all  closely  their  pre- 
determined standard  distribution.  The  mechanical  and  unin- 
telligent application  of  a  standard  distribution  by  some  instruc- 
tors has  given  the  opponents  of  the  plan  concrete  examples  of  what 
they  imagined  to  be  the  normal  result  of  its  use. 

A  standard  distribution  is  merely  a  device  which  teachers 
may  use  in  order  to  reduce  to  a  minimum  the  constant  errors  in 
their  grades,  but  to  be  helpful  it  must  be  used  intelligently.  It 
must  be  remembered  that  a  standard  distribution  is  a  means  and 

[51] 


not  an  end.  Whenever  common  sense  Indicates  that  the  distribu- 
tion of  grades  for  a  particular  class  should  depart  from  the  normal 
distribution  no  instructor  should  hesitate  to  award  the  grades 
which  he  believes  the  students  deserve.  It  is  intended  that  the 
standard  distribution  will  be  closely  approximated  only  for  a  large 
unselected  group  of  students.  A  particular  class  very  frequently 
is  made  up  of  a  selected  group  of  students.  Furthermore,  classes 
of  the  usual  size,  20  to  35,  are  so  small  that  frequently  there  will  be 
significant  departures  from  this  standard  distribution. 

Translating  scores  into  school  marks  by  means  of  a  standard 
distribution.  A  standard  distribution  is  useful  in  translating  ex- 
amination "scores"  into  "grades."  The  examination  papers  should 
be  marked  in  terms  of  a  score.  This  score  may  or  may  not  be  on 
the  scale  of  100  points.  In  order  to  avoid  confusion  between 
"scores"  and  "grades"  it  is  wise  to  use  a  scale  of  points  shown  so 
that  the  maximum  score  will  not  be  100.  If  the  papers  have  been 
marked  in  this  way  the  scores  may  be  arranged  in  col- 
umns as  indicated  in  the  left  hand  margin.  The  first  step 
in  translating  these  scores  into  grades  is  to  determine 
whether  or  not  the  class  is  typical.    If  an  experienced 


69 
68 
64 

63 
60 


58 
57 
56 
55 
54 
51 
50 


38 
35 

32 


teacher  has  had  a  class  for  several  weeks  he  will  usually 
be  able  to  estimate  its  general  status  with  a  fair  degree 
of  accuracy.  •  At  the  beginning  of  a  school  year  or  in  the 
case  of  an  inexperienced  teacher  some  outside  informa- 

—  tion  is  needed.  The  previous  school  record  of  the  stu- 
dents may  be  studied  but  in  many  cases  it  will  be  more 
convenient  to  administer  a  general  intelligence  test.   The 

r-.  average  mental  age  and  the  distribution  of  the  I.Q.'s  of 
the  class  will  be  a  very  reliable  index  of  the  composition 
of  the  group.  If  the  median  I.Q.  is  distinctly  below  100 
the  teacher  may  know  that  he  has  poor  pupil  material. 
If  it  is  much  above  100  he  knows  that  the  class  consists  of 
pupils  better  than  the  average.  If  there  is  an  unusually 
high  number  of  low  I.Q.'s  he  may  expect  a  relatively 
high  number  of  low  grades. 

With  the  general  status  of  the  class  in  mind  the 
scores  may  be  grouped  in  conformity  with  the  system  of 
marks  used.  In  the  illustration  in  the  left  hand  margin 
it  has  been  assumed  that  the  class  is  approximately  typi- 
cal.   The  percent  of  A's  and  also  the  percent  of  failures 

[52] 


are  somewhat  larger  than  the  percent  specified  in  most  standard 
distributions.  If  the  scores  are  arranged  in  the  form  shown  be- 
low the  general  shape  of  the  distribution  will  be  more  obvious. 
However,  in  the  majority  of  cases  it  will  be  sufficient  to  use  the 
arrangement  given  in  the  margin. 

58 

57 

47     56  69 

46     55  68 

38     42     54  64     74 

35     41     51  63     73 

32    40     50  60     70 

E      D     C  B      A 

It  is  seldom  that  one  will  have  exactly  a  symmetrical  distri- 
bution of  grades  for  a  class  of  this  size.  Some  departures  from  the 
standard  distribution  must  be  expected.  In  case  the  class  is  not 
typical  one  should  expect  marked  departure  from  the  standard 
distribution.  For  example,  the  distribution  for  a  given  class 
might  be  as  shown  below.  In  this  there  are  no  grades  below  passing 
but  there  are  a  number  of  poor  students  just  above  the  passing 
mark.  Also  the  percent  of  A's  and  B's  is  unusually  large.  Such  a 
distribution  is  not  normal  but  might  well  represent  the  distribution 
of  grades  for  a  particular  class  even  when  the  normal  distribution 
had  been  adopted  as  the  standard.  If  the  teacher  is  able  to  show 
that  the  general  status  of  the  class  justifies  such  a  departure  he 
deserves  commendation  rather  than  criticism  for  his  distribution. 

64 

42  63 

41  54  60  74 

40  51  58  73 

38  50  57  70 

35  47  56  69 

32  46  55  68 

E      D  C  B  A 

An  accumulative  distribution  used  as  a  check  upon  constant 
errors.  A  standard  distribution  is  also  useful  as  a  check  upon  the 
grades  given  by  a  teacher  over  a  period  of  several  terms.  When  the 
grades  for  the  entire  period  are  assembled  in  such  a  distribution 
any  general  tendency  on  the  part  of  the  teacher  to  give  too  high 
or  too  low  grades  will  be  revealed.    Each  teacher  should  keep  an 

[S3] 


accumulative  distribution  of  the  grades  in  each  subject  he  teaches. 
For  example,  a  teacher  in  mathematics  should  keep  an  accumula- 
tive distribution  of  the  grades  given  in  classes  of  first-year  algebra. 
When  the  total  number  of  grades  becomes  large  a  comparison  of 
this  distribution  with  the  standard  distribution  will  reveal  any 
tendency  on  the  part  of  the  teacher  to  grade  too  high  or  too  low 
in  this  subject.  A  teacher  should  then  take  steps  to  correct  any 
marked  departures  from  the  practise  defined  by  the  standard  dis- 
tribution. In  large  schools  where  there  are  several  sections  of  the 
same  subject  it  will  be  helpful  to  secure  a  distribution  of  grades 
each  time  they  are  issued.  Any  marked  departures  from  the 
standard  distribution  will  then  be  called  to  the  attention  of  the 
teachers.  However,  one  should  avoid  giving  the  impression  that 
there  must  be  uniformity  with  the  standard  distribution.  De- 
partures from  this  standard  distribution  are  justified  when  the 
group  of  pupils  can  be  shown  to  be  selected.  Thus  a  departure 
from  the  standard  distribution  is  a  cause  for  an  investigation  on 
the  part  of  the  teachers  concerned.  If  evidence  can  be  produced 
which  justifies  the  departure  no  change  in  the  system  of  grading 
should  be  used.  On  the  other  hand  when  investigation  reveals  no 
reasons  why  there  should  be  departures  from  the  standard  dis- 
tribution, the  teachers  should  be  urged  to  modify  their  system  of 
grading  so  that  a  greater  uniformity  will  be  secured. 

2.  Decreasing  the  variable  errors  in  examination  scores. 
The  reduction  of  the  magnitude  of  variable  errors  of  measurement 
in  examination  scores  is  to  be  secured  mainly  through  the  adop- 
tion of  rules  which  will  bring  about  greater  uniformity  in  preparing 
and  administering  examinations.  These  rules  should  include 
specifications  in  regard  to  the  effect  of  poor  writing,  poor  spelling, 
and  poor  English  upon  a  student's  grade,  and  should  be  in  agree- 
ment in  regard  to  giving  credit  for  correct  principle  and  partial 
credit  for  exercises  partly  right  or  partly  completed.  The  rules 
may  properly  include  also  specifications  relating  to  the  number  and 
types  of  questions  to  be  asked  and  the  form  in  which  they  are  to  be 
presented  to  the  students.  For  guidance  in  marking  papers  a 
teacher  should  write  out,  at  least  in  abbreviated  form,  the  cor- 
rect answers  to  the  questions.  The  accuracy  of  examination  scores 
will  be  increased  also  by  making  the  examinations  more  uniform 
with  respect  to  content.* 

*For  recommended  rules  covering  these  and  other  points  see  Chapter  VII. 

[54] 


It  has  been  proposed  that  the  use  of  types  of  questions  which 
call  for  answers  that  may  be  objectively  classified  as  either  "right" 
or  "wrong,"  would  facilitate  uniformity  in  marking  the  papers. 
This  means  of  reducing  the  variable  errors  of  measurement  will 
be  considered  under  the  head  of  "simplifying  the  administration 
of  written  examinations." 

3.  Securing  agreement  of  the  content  of  examinations  with 
recognized  educational  objectives.  The  intrinsic  function  of  an 
examination  is  to  measure  certain  achievements.  In  general  the 
achievements  for  which  we  desire  to  secure  measurements  are  those 
included  in  the  recognized  educational  objectives.  Hence,  the 
questions  should  be  in  agreement  with  the  objectives.  Therefore, 
it  is  impossible  to  cover  all  details  in  a  given  subject-matter  field. 
The  questions  should  relate  to  the  most  significant  facts,  princi- 
ples, etc.  of  the  course.  Catch  questions  and  those  calling  for  un- 
important details  have  no  place  in  an  examination.  For  example, 
an  examination  in  spelling  should  not  include  unusual  or  obsolete 
words,  an  examination  in  history  should  not  call  for  obscure  dates 
or  other  trivial  facts. 

In  securing  agreement  the  teacher  should  make  use  of  such 
terms  of  minimum  essentials  as  are  available.  For  example,  in 
spelling  a  teacher  may  very  properly  select  the  test  words  from 
Ayres'  list  of  the  one  thousand  most  frequently  used  words  or 
from  some  other  carefully  prepared  minimum  essential  list.  In 
geography  a  teacher  will  find  the  Hahn-Lackey  Geography  Scale 
a  helpful  source  of  questionings.  In  other  subjects  the  teacher  will 
not  have  access  to  terms  of  minimum  essentials  as  complete  as  in 
these  two  subjects,  but  he  should  become  familiar  with  curriculum 
studies  and  other  investigations^  relating  to  educational  objectives. 


^The  following  list  is  suggestive  of  studies  relating  to  educational  objectives: 

Yearbooks  of  the  National  Society  for  the  Study  of  Education.  Bloomington,  Illi- 
nois:  Public  School  Publishing  Company. 

Part  I  of  14th — reading,  writing,  spelling,  language  and  grammar,  arithmetic,  history, 
literature,  geography. 

Part  I  of  16th — reading,  writing,  spelling,  arithmetic,  history,  physical  education. 

Part  I  of  17th — arithmetic,  geography,  reading,  English,  civics,  history. 

Part  II  of  17th — history,  civics,  economics,  sociology,  geography. 

Part  I  of  19th — on  new  materials  of  instruction,  reading,  history,  geography,  mathe- 
matics, nature  study,  civics. 

Part  I  of  20th — on  materials  of  Instruction — all  subjects  in  elementary  schools. 

Part  II  of  22nd— the  social  studies  in  the  elementary  and  secondary  school. 

"Arithmetic,  course  of  study  for  the  elementary  schools.  Including  the  kindergarten 
and  the  first  six  grades."  Course  of  Study  Monographs,  Elementary  Schools, 
No.  1  Berkeley,  California:  Public  Schools,  1921.     86p.     {Concluded  on  p.  56.) 


In  some  subjects  there  are  valuable  committee  reports  which  give 
the  consensus  of  opinion  concerning  the  relative  importance  of  the 
numerous  distributions. 

The  teacher  must  assume  most  of  the  responsibility  for  se- 
curing the  agreement  between  the  content  of  the  examination  and 
educational  objectives.  In  many  of  the  high-school  subjects  he 
can  obtain  little  assistance  from  such  sources  as  just  indicated. 
However,  if  this  purpose  is  kept  in  mind  and  if  he  is  really  famil- 
iar with  the  subject  which  he  is  teaching,  gross  inconsistencies 
with  recognized  educational  objectives  will  be  avoided. 

4.  Simplifying  the  administration  of  written  examinations. 
The  administration  of  written  examinations,  particularly  the 
marking  of  the  papers,  can  be  greatly  simplified  by  the  use  of 
certain  types  of  exercises.  For  example,  in  the  true-false  type  of 
exercise  the  pupil  merely  indicates  whether  the  statement  is  true 
or  false.  Instead  of  asking  the  question,  "Why  did  the  Puritans 
come  to  America  in  the  seventeenth  century?"  we  may  ask 
whether  the  following  statement  is  true  or  false.  "The  Puritans 
came  to  America  in  the  seventeenth  century  seeking  wealth." 
The  pupil  may  give  his  answer  to  this  exercise  by  writing  a  plus 
sign  after  the  statement  if  he  considers  it  true  and  a  minus  sign  if 
he  considers  it  false.  In  case  the  statement  is  dictated  to  him 
he  may  write  after  the  number  of  the  exercise  the  word  "true" 
or  "false"  or  the  appropriate  sign.  The  answering  of  such  exer- 
cises requires  very  little  of  the  pupil's  time  and  the  scoring  is  ex- 
ceedingly simple.  Questions  which  can  be  answered  merely  by 
"yes"  or  "no"  also  simplify  the  administration  of  examinations. 
Similar  results  can  be  secured  with  recognition  exercises  such  as 
have  been  used  in  a  number  of  standardized  silent  reading  tests. 
The  following  is  an  exercise  of  this  type. 

Ayres,  L.  P.  "A  measuring  scale  for  ability  in  spelling."  N.  Y.:  Division  of  Education, 

Russell  Sage  Foundation,  1915.    58p. 
Ayres,  L.  P.     "Measuring  scale  for  handwriting."    N.  Y.:     Division  of  Education, 

Russell  Sage  Foundation,  1920.    (Folder,  chart.) 
Bagley,  W.  C.  and  Rugg,  H.  O.    "The  content  of  American  history  as  taught  in  the 

seventh  and  eighth  grades."  University  of  Illinois  Bu!letin,Vol.  13,  No.  51.  Urbana: 

University  of  Illinois. 
Charters,  W.  W.    Curriculum  Construction.    N.  Y.:    Macmillan  Co.,  1923.    352p. 
Charters,  W.  W.  and  Miller,  Edith.    "A  course  in  grammar."   University  of  Missouri 

Bulletin,  Vol.  I,  Education  Series  9.    Columbus:   University  of  Missouri,  1915. 
Hahn,  H.  H.    Hahn-Lackey  Geography  Scale.  Wayne,  Nebraska:  H.  H.  Hahn,  State 

Normal  School. 
Hahn,  H.  H.    Scale  for  Measuring  Ability  of  Children  in  History.    Wayne,  Nebraska: 

H.  H.  Hahn,  State  Normal  School. 
Moore,  E.C.    Minimum  Course  of  Study.    N.  Y.:  Macmillan,  1923.  402p. 

[56] 


"The  first  president  of  the  United  States  was:  Christo- 
pher Columbus,  Benjamin  Franklin,  George  Washington, 
Thomas  Jefferson." 
In  answering  this  exercise  the  pupil  is  asked  to  underline  or  mark 
in  some  other  way  the  name  required  to  make  a  true  sentence. 
Completion  exercises  in  which  pupils  are  asked  to  supply  words 
which  have  been  omitted  furnish  still  another  means  of  simplifi- 
cation. 

Directions  for  constructing  a  true-false  examination.^  1.  In 
constructing  true-false  exercises,  a  list  of  statements  covering  in 
some  detail  the  portion  of  the  subject  on  which  the  pupils  are  to  be 
examined  should  be  prepared.  Some  of  the  statements  can  then 
easily  be  changed  so  that  they  are  false.  The  untruth  of  a  state- 
ment should  not  be  too  obvious  or  it  will  be  worthless  for  testing. 
Also  statements  should  be  selected  which  require  an  acquaintance 
with  the  subject  in  order  to  determine  their  truth  or  falsity. 

2.  In  a  true-false  examination  the  number  of  true  statements 
should  approximate  the  number  of  false  statements,  and  the 
arrangement  should  be  such  that  there  is  no  regular  sequence  be- 
tween true  statements  and  false  statements. 

3.  Since  the  pupil  can  give  his  responses  very  quickly,  the 
examination  should  consist  of  not  less  than  fifty  statements.  A 
true-false  examination  of  one  hundred  statements  can  be  given  in 
the  time  usually  devoted  to  an  ordinary  examination. 

4.  The  examination  should  be  mimeographed  or  printed  so 
that  each  pupil  will  have  a  copy.  He  may  give  his  answers  in  the 
margins  of  the  sheets,  or,  if  it  is  desired  to  use  the  same  set  of 
papers  with  another  group  of  pupils,  he  may  be  given  a  sheet  of 
paper  on  which  there  are  numbered  blanks.  The  pupils  will  then 
be  asked  to  record  in  the  blanks  their  answers  to  the  corresponding 
exercises.  'A  less  desirable  plan,  which  may  be  followed  when  it  is 
not  possible  to  secure  mimeographed  copies  of  the  examination,  is 
to  read  the  statements  to  the  pupils  and  have  them  record  their 
answers  in  numbered  blanks.  The  disadvantage  of  this  plan  is 
that  the  pupils  do  not  have  a  satisfactory  opportunity  to  study  the 
statements.  _^lso  the  class  may  give  some  indication  of  the  answer 
if  a  statement  appeals  to  them  as  being  ridiculous. 

5.  The  pupils  should  be  given  specific  directions  in  regard  to 
answering  exercises  about  which  they  are  uncertain.    One  writer 


*For  an  example  of  a  true-false  examination,  see  Appendix  p.  69. 

[57] 


has  suggested  that  the  pupils  be  instructed  to  guess  concerning  the 
truth  or  falsity  of  the  statement.  Another  writer  who  has  used 
this  type  of  examination  instructed  the  pupils  as  follows:  "First, 
go  through  the  list  quickly  and  mark  all  that  you  know  for  certain, 
then  go  back  and  study  out  the  harder  ones.  Do  not  guess;  the 
chances  are  against  you  on  guessing.  Don't  endanger  your  score 
by  gambling  on  those  questions  about  which  you  know  nothing." 
This  second  procedure  is  probably  the  better. 

The  scoring  of  a  true-false  examination.  Since  only  two  re- 
sponses are  possible,  it  is  obvious  that  a  pupil  may  give  a  correct 
response  as  the  result  of  chance.  In  order  to  take  this  possibility 
into  account,  a  pupil's  score  on  an  examination  of  this  type  is  the 
number  of  exercises  answered  correctly  minus  the  number  answer- 
ed incorrectly.    Exercises  not  attempted  are  not  counted. 

Directions  for  constructing  a  recognition  examination.'  In 
constructing  this  type  of  examination  none  of  the  proposed  an- 
swers should  be  too  obviously  incorrect.  An  exercise  can  yield  an 
indication  of  a  pupil's  achievement  only  when  he  is  forced  to  use 
judgment  in  determining  which  of  the  proposed  answers  is  suit- 
able. For  example,  the  illustrative  exercise  given  would  be  practi- 
cally worthless  for  testing  purposes  if  all  the  names,  except  that  of 
George  Washington,  were  of  persons  living  today  or  of  persons 
having  no  connection  with  our  national  life.  In  applying  this  type  of 
exercise  to  the  field  of  arithmetic  the  proposed  answers  should  include 
erroneous  answers  which  pupils  are  inclined  to  give:  if  the  exercise 
called  for  the  quotient  of  two  fractions,  one  of  the  proposed  an- 
swers should  be  the  product  of  the  fractions  and  another  their  sum, 
and  perhaps  another  should  be  the  fraction  obtained  by  taking 
the  sum  of  the  numerators  as  a  new  numerator  and  the  sum  of  the 
denominators  for  a  new  denominator.  When  the  correct  answer  is 
included  in  a  group  of  such  answers  as  these,  the  pupil  who  does 
not  know  how  to  find  the  quotient  of  such  fractions  will  be  unable 
to  determine  the  correct  answer  except  as  a  matter  of  chance. 
On  the  other  hand,  if  all  of  the  answers  except  the  correct  one  were 
integers  or  were  so  large  that  they  were  obviously  incorrect,  a 
bright  pupil  who  knew  nothing  about  division  of  fractions  would 
be  able  to  select  the  correct  answer.  The  correct  answer  should 
not  always  be  found  in  the  same  position;  sometimes  it  should  be 


'For  an  example  of  a  recognition  examination  see  Appendix  p.  75. 

[58] 


first,  sometimes  last,  and  sometimes  in  an  intermediate  position. 
As  in  the  case  of  the  true-false  examination,  a  recognition  ex- 
amination should  consist  of  a  large  number  of  exercises. 

Examinations  of  this  type  should  be  mimeographed  or  printed 
and  each  pupil  should  have  a  copy.  Definite  instructions  concern- 
ing methods  of  work  should  be  given.  It  is  probably  best  to  in- 
struct the  pupil  to  work  through  the  test  rapidly,  answering  those 
exercises  about  which  he  is  certain.  He  should  then  go  back  over 
the  list  and  try  the  more  difficult  ones.  Not  fewer  than  four  pro- 
posed answers  should  be  included  in  each  statement  and  the 
pupils  may  be  instructed  to  guess  if  they  do  not  know,  since  the 
chance  of  success  by  guessing  is  slight.  The  pupil's  score  on  an 
examination  of  this  type  may  be  taken  as  the  number  of  exercises 
done  correctly. 

A  somewhat  unusual  but  interesting  type  of  recognition  ex- 
ercise is  that  described  as  a  "matching  contest."  In  this  a  pupil 
is  given  two  lists  of  statements,  the  first  numbered  1,  2,  3,  4,  5, 
etc.,  the  second  marked  A,  B,  C,  D,  E,  etc.  In  the  second  list, 
there  is  a  statement  which  corresponds  in  meaning  to  a  statement 
in  the  first  list  and  the  pupil  is  to  pair  these  statements,  marking 
by  the  number  of  the  first  list  the  letter  of  the  corresponding  state- 
ment of  the  second.  For  example,  in  the  exercises  given  below: 
by  the  date  marked  (5),  1898,  we  place  the  letter  B  to  indicate  the 
event  for  which  that  date  is  significant.  It  is  difficult  to  construct 
such  examinations  so  that  they  will  require  reasoning  on  the  part 
of  the  student.  Their  most  important  use  is  in  the  elementary 
school  for  rapid  drill  in  certain  phases  of  some  subjects,  such  as 
definitions  in  geography  and  grammar,  etc.  The  following  exer- 
cises, selected  from  the  Spokane  United  States  History  Test, 
illustrate  the  use  of  such  an  examination  in  linking  a  certain  date 
or  person  with  the  corresponding  event. 


1.  1846 

2.  1865 

3.  1863 

4.  1917 

5.  1898 

6.  1789 

7.  1792 

8.  1776 

9.  1861 
10.  1914 


A.  Lincoln's  Emancipation  Proclamation 

B.  Spanish-American  War 

C.  Beginning  of  World  War 

D.  Declaration  of  Independence 

E.  United  States  entered  World  War 

F.  Election  of  Washington  as  President 

G.  War  with  Mexico  began 
H.  Invention  of  the  cotton  gin 

I.  Lee's  surrender  at  Appomattox 

J.  Beginning  of  Civil  War 

[59] 


1.  Foch 

2.  Lincoln 

3.  Fulton 

4.  Dewey 

5.  Pershing 

6.  Bell 

7.  Edison 

8.  Jefferson 

9.  Lee 

10.  Franklin 


A.  Destroyed  Spanish  fleet  in  Manila  Bay 

B.  Invented  the  telephone 

C.  Leading  Confederate  General 

D.  Wrote  the  Declaration  of  Independence 

E.  Invented  the  steamboat 

F.  Commanded  allied  armies  in  the  World  War 

G.  Was  President  during  the  Civil  War 

H.  Commanded  American  Forces  in  the  World  War 

I.  Was  Revolutionary  patriot,  author,  and  inventor 

J.  America's  most  famous  inventor 


Directions  for  constructing  completion  exercises.^  A  com- 
pletion exercise  should  be  constructed  so  that  no  suggestion  will  be 
given  of  the  correct  words  to  be  written  in  the  blanks.  Further- 
more, the  facts  to  be  supplied  should  be  important.  The  best 
plan  is  to  prepare  a  list  of  important  statements  and  principles 
covering  the  portion  of  the  subject  over  which  the  pupils  are  to  be 
examined  and  then  from  these  statements  to  strike  out  a  certain 
significant  word  or  phrase.  In  every  case,  if  it  is  possible,  the 
words  omitted  should  be  such  that  only  one  answer  will  be  correct. 
Since  little  writing  is  required  of  the  pupils  they  may  be  asked  to 
fill  in  as  many  as  one  hundred  blanks. 

The  scoring  of  completion  exercises  is  not  as  highly  objective 
as  in  the  two  types  mentioned  above.  Pupils  will  tend  to  write  a 
variety  of  words  in  the  blanks.  Different  words  may  have  almost 
the  same  meaning,  and  frequently  the  scorer  will  be  compelled  to 
determine  whether  the  meaning  of  some  word  is  sufficiently  near 
that  of  the  correct  answer  to  justify  giving  the  pupil  credit  for 
having  answered  the  exercises  correctly.  However,  by  a  careful 
selection  of  statements  and  of  the  omitted  words,  this  subjectivity 
may  be  greatly  minimized.  For  example,  in  the  sentence,  "The 
first  Continental  Congress  was  held  in  ...  .,"  only  one 
possible  word  can  be  correct.  In  using  completion  exercises  it  is 
necessary  to  provide  each  pupil  with  a  mimeographed  or  printed 
copy  of  the  examination.  The  pupil's  score  is  the  number  of 
blanks  filled  in  correctly. 

Advantages  of  the  "new  examination."  Examinations  con- 
sisting of  exercises  of  the  types  described  above  have  certain  ob- 
vious advantages.  There  will  be  a  large  saving  of  time  for  both 
teacher  and  pupil.    The  pupil  is  called  upon  to  do  little  or  no 


*For  an  example  of  a  completion  examination  see  Appendix  p.  73. 

[60] 


writing  in  giving  his  answers  and  therefore  is  able  to  respond  to  a 
large  number  of  exercises.  The  teacher  in  scoring  will  have  little 
or  no  occasion  to  use  judgment  as  he  will  need  only  to  note  the 
brief  responses  given  by  the  pupils.  Thus  the  labor  of  scoring  will 
be  greatly  reduced  and,  more  important,  the  scoring  will  be  much 
more  highly  objective  than  that  in  the  marking  of  examination 
papers  of  the  usual  type.  The  saving  of  time  in  the  giving  and 
scoring  of  the  "new  examination"  will  more  than  offset  any  ad- 
ditional time  that  may  be  expended  in  its  construction.  Another 
advantage  is  that  the  new  examination  can  be  made  more  com- 
prehensive. Examinations  as  a  rule  consist  of  ten  questions.  Some 
are  limited  to  a  smaller  number.  Consequently  the  scope  of  ex- 
aminations of  the  traditional  type  is  necessarily  narrow.  "New 
examinations"  of  the  true-false  type  should  consist  of  not  less  than 
fifty  exercises  and  may  have  as  many  as  one  hundred.  Other  types 
of  the  "new  examination"  should  be  of  a  corresponding  length. 
Hence  a  "new  examination"  will  usually  be  more  comprehensive 
than  a  traditional  examination. 

Limitations  of  the  "new  examination."  There  are  certain 
limitations  of  the  new  examination  which  should  be  noted  along 
with  its  advantages.  It  can  not  be  used  in  mathematics  except  to  a 
limited  extent.  It  can  not  be  used  at  all  in  English  Composition. 
In  other  subjects  there  are  many  phases  of  achievement  which  are 
not  measured  directly  by  examinations  made  up  of  exercises  of  the 
types  described  above.  Hence,  altho  the  "new  examination"  is 
more  comprehensive  with  reference  to  information,  and  does  meas- 
ure certain  types  of  achievements,  it  is  likely  that  pupils  would 
miss  much  valuable  experience  and  training  if  they  were  not  at 
times  asked  to  "compare,"  "explain,"  "discuss,"  "define,"  or 
"tell  why."  They  should  also  be  asked  to  summarize  material 
presented  on  a  topic  or  to  apply  certain  principles.  The  following 
questions  taken  from  Hahn's  Scale  for  Measuring  Ability  of 
Children  in  History  appear  to  require  mental  processes  distinctly 
different  from  those  called  for  by  the  "new  examination." 

1.  "State  points  of  similarity  between  the  position  of  the  United 
States  in  1812  and  their  position  in  1912." 

2.  "Arrange  the  following  events  in  order  of  cause  and  effect: 
Force  Bill,  Carpet  Baggers,  Fifteenth  Amendment,  Negro  Rule  in 
Some  of  the  Southern  States,  Ku  Klux  Klan." 

3.  "Name  the  presidents  of  the  United  States  since  1892." 

[61] 


An  intelligent  attitude  toward  the  "new  examination."    The 

simple  administration  of  the  new  examination  and  other  attrac- 
tive features  should  not  blind  one  to  the  limitations  just  mention- 
ed. As  indicated  in  Chapter  II  written  examinations  do  more 
than  merely  secure  measures  of  achievement.  If  they  consist  of  the 
right  kind  of  exercises  they  afford  significant  educational  oppor- 
tunities. The  educational  opportunities  of  the  "new  examination" 
are  necessarily  restricted,  and  it  would  be  unfortunate  if  it  entirely 
replaced  examinations  of  the  traditional  type.  The  new  examina- 
tion, however,  has  a  place.  It  may  be  used  occasionally  in  most 
school  subjects.  It  is  useful  when  a  teacher  wishes  to  test  the 
acquaintance  of  a  class  with  a  wide  range  of  facts.  It  has  little 
diagnostic  value  and  examinations  of  the  traditional  type  should 
be  used  when  information  is  desired  concerning  the  weaknesses 
of  different  members  of  a  class.  For  this  reason  the  "new  exami- 
nation" is  more  appropriate  for  use  at  the  end  of  a  term  than  for 
tests  during  the  term  which  have  as  their  purpose  both  measure- 
ment and  diagnosis. 


[62] 


CHAPTER  VII 

RULES  FOR  THE  PREPARATION  AND  ADMINISTRATION 
OF  WRITTEN  EXAMINATIONS. 

Below,  a  group  of  suggested  rules  governing  the  preparation 
and  administration  of  written  examinations  are  given.  These 
represent  the  opinion  of  the  writers  which  is  based  upon  a  careful 
study  of  the  problems  involved,  as  well  as  upon  several  years  of 
experience  in  the  measurement  of  school  achievement. 

1.  Final  examinations  should  be  required.  In  school  subjects 
such  as  shop  work,  in  which  the  performances  secured  from  pupils 
are  highly  objective,  the  waiving  of  this  requirement  may  be  justi- 
fied. When  final  examinations  are  given  no  student  should  be 
excused  from  them  because  of  high  daily  grades,  deportment  or 
attendance.    (See  p.  16) 

2.  The  content  of  final  examinations  should  agree  as  closely 
as  possible  with  recognized  educational  objectives.  In  fields  where 
minimum  essentials  have  been  determined  they  should  be  used  as 
a  basis  in  formulating  questions.    (See  p.  55) 

3.  The  questions  should  be  definite  and  stated  so  that  all 
pupils  will  interpret  them  alike.  Questions  relating  to  items  of 
minor  importance  should  occupy  a  minor  place  in  examinations. 
Questions  relating  to  points  which  have  not  received  attention  in 
the  course  should  be  omitted.^    (See  also  rule  11.) 

4.  When  the  necessary  equipment  is  available  the  questions 
should  be  mimeographed  or  typewritten  so  that  each  student  will 
have  a  copy  on  his  desk.  In  case  they  are  written  on  the  board  the 
teacher  should  make  certain  that  all  pupils  are  able  to  read  them 
correctly.  It  is  well  in  either  case  to  read  the  questions  aloud  to 
the  class. 

5.  The  examination  should  be  sufficiently  difficult  so  that 
few  pupils  will  make  perfect  scores.  (This  rule  should  not  apply 
<J 

frequently  in  an  examination  the  difficulty  of  the  question  is  due  to  the  lack  of 
emphasis  placed  upon  it  throughout  the  term  because  it  deals  with  a  relatively  un- 
important topic.  Other  topics,  difficult  in  themselves,  but  emphasized  because  of 
their  importance,  furnish  the  easier  questions. 

[63] 


when  the  purpose  of  the  examination  is  to  determine  which  stud- 
ents have  attained  a  given  standing  which  includes  perfection  of 
performance.)    (See  p.  12) 

6.  Usually  the  examination  should  be  long  enough  so  that 
every  member  of  the  class  will  be  kept  busy  for  the  entire  period. 
It  is  better  to  make  the  examination  too  long  than  to  have  it  too 
short.  In  this  way  it  becomes  possible  also  to  take  into  account 
the  student's  rate  of  work  in  determining  his  grade.  Appropriate 
adjustments  can  be  made  in  interpreting  "scores"  into  school 
"marks."    (See  p.  22  and  13) 

7.  In  questions  asking  for  a  discussion  or  explanation  indi- 
cate the  completeness  of  the  discussion  or  the  degree  of  elaborate- 
ness expected  in  the  answer.    (See  p.  24) 

8.  Time  may  be  economized  for  both  students  and  teacher  by 
using  some  form  of  the  "new  examination."  This  type  of  measur- 
ing instrument,  however,  possesses  certain  limitations  which 
should  be  kept  in  mind.  The  exclusive  use  of  it  would  be  unwise. 
(See  p.  61) 

9.  Unless  the  students  have  a  definite  understanding  of  the 
methods  of  work  which  are  to  be  followed,  the  teacher  should  give 
them  explicit  directions  concerning  such  matters  as  the  order  in 
which  the  questions  are  to  be  answered,  the  desired  arrangement 
of  the  work,  and  any  other  items  in  which  there  is  an  opportunity 
for  pupils  to  adopt  different  procedures.  (In  the  case  of  most 
standardized  educational  tests,  the  directions  to  students  are  very 
detailed  and  explicit.)    (See  p.  24) 

10.  Approximately  ninety  minutes  should  be  allowed  for  a 
final  examination  in  most  high-school  subjects.  The  time  which 
teachers  should  devote  to  the  preparation  of  the  questions  will  de- 
pend upon  their  experience  and  upon  their  practise  during  the 
semester.  It  is  recommended  that  a  teacher  make  a  record 
throughout  the  term  of  questions  which  in  his  judgment  are 
suitable  for  a  final  examination.  From  two  to  three  hours  should 
be  sufficient  for  marking  a  set  of  twenty-five  examination  papers. 
If  a  teacher  finds  that  a  longer  time  is  required,  he  should  en- 
deavor to  modify  his  procedure  so  that  this  work  can  be  done 
more  quickly.    (See  p.  19) 

11.  Altho  any  weighting  of  questions  by  a  teacher  will  be 
subjective,  it  is  probably  desirable  to  weight  the  questions,  par- 
ticularly in  cases  of  extreme  differences  in  value.    The  weighting, 

[64] 


ho  vever,  should  be  upon  the  basis  of  social  importance  rather  than 
upc  1  mere  difficulty.    (See  p.  22) 

2.  It  is  advisable  for  the  teacher  to  write  out  at  least  in  an 
abbreviated  form  the  answers  to  examination  questions  before  he 
begins  marking  the  papers.  In  mathematics  and  other  subjects 
where  a  definite  answer  is  required  and  only  one  can  be  accepted 
as  correct,  the  need  for  this  rule  is  not  as  great  as  in  such  subjects 
as  geography,  history,  literature  and  certain  phases  of  science. 
However,  a  list  of  correct  answers  will  usually  mean  a  saving  of 
time.    (See  p.  23) 

13.  Except  in  courses  in  English  a  pupil's  grade  should  not  be 
intentionally  lowered  for  errors  in  spelling  or  for  poor  handwriting. 
As  a  rule  the  grade  should  not  be  lowered  because  of  poor  English, 
unless  the  quality  of  the  English  is  evidence  of  unsatisfactory 
reasoning.  Rules  covering  these  points,  as  well  as  others  con- 
cerning which  teachers  might  differ,  should  be  formulated  by  the 
principal  in  conference  with  his  teachers  or  at  least  a  committee 
of  them.  The  rules  thus  formulated  should  be  carefully  followed 
by  all  of  the  teachers.    (See  p.  20) 

14.  In  marking  the  papers  more  accurate  results  will  in  gen- 
eral be  secured  if  the  answers  to  one  question  are  marked  on  all 
the  papers  before  those  for  another  question  are  taken  up.  (See 
p.  23)  When  it  is  desired  to  mark  all  of  the  questions  on  one  paper 
before  taking  up  another,  the  "sorting  method"  should  be  used. 
According  to  this  procedure  the  papers  as  they  are  read  are  sorted 
into  piles,  the  best  ones  being  placed  in  the  first  pile,  the  next  best 
in  second  pile,  etc.  Five  distributions  will,  in  most  cases,  prove 
sufficient.  After  all  the  papers  have  been  distributed  they  should 
be  reread,  one  pile  at  a  time,  and  compared  with  each  other.  If 
these  papers  do  not  possess  approximately  the  same  value,  changes 
in  the  sorting  may  be  made.  Grades  may  then  be  assigned  to  the 
papers  in  the  different  piles. 

15.  The  distinction  between  "scores"  and  "grades"  should  be 
kept  in  mind.  (See  p.  11)  The  papers  should  be  marked  first 
in  terms  of  scores.  In  doing  this  an  appropriate  number  of  points 
should  be  determined  for  each  question.  It  is  not  necessary  that 
the  total  of  these  points  be  100.    (See  p.  52) 

16.  The  point  scores  assigned  to  the  examination  papers 
should  be  translated  into  school  marks.  In  doing  this  the  use  of  a 
standard  distribution  will  be  found  helpful,  and  will  operate  also 
to  decrease  the  magnitude  of  the  constant  errors.    (See  p.  50) 

[65] 


APPENDIX 

(Questionnaire  Sent  to  High-School  Teachers) 

QUESTIONNAIRE  RELATING  TO  THE  USE  OF  WRITTEN  EXAMINA- 
TIONS IN  HIGH  SCHOOLS 

Teacher High  School City , 


The  major  subject  which  I  am  teaching  Is. 


The  following  questions  are  to  be  answered  only  with  reference  to  the 
major  subject  you  are  teaching. 

1.  Approximately  how  much  time  do  you  use  in  preparing  questions 
for  a  final  examination  which  the  students  are  allowed  a  total  of  90  min- 
utes to  answer? Min. 

("Final  examination"  as  used  in  this  questionnaire  means  an  examination 
which  is  given  at  the  end  of  a  semester  and  which  is  based  on  the  work  of 
the  entire  semester.) 

2.  In  preparing  a  set  of  examination  questions  do  you  usually  at- 
tempt to  arrange  these  questions  in  order  of  ascending  difficulty? Yes     No* 

3.  Do  you  prepare  in  written  form  carefully  worded  directions  to  the 
students  regarding  the  procedure  they  are  to  follow  in  answering  the 
questions?  (These  directions  might  include  such  points  as,  order  in  which 
questions  are  to  be  answered,  length  of  answers,  arrangement  of  work,  etc.)   Yes     No 

4.  Which  of  the  following  methods  do  you  use  in  presenting  ques- 
tions to  the  student? 


(a)  Writing  the  questions  on  the  board Yes     No 

(b)  Furnishing  the  pupils  with  a  mimeographed,  carbon  or 

printed  copy  of  the  questions Yes    No 

(c)  Dictating  the  questions  to  the  pupils Yes     No 

5.  Is  it  your  custom  to  make  the  examination  long  enough  so  that 
practically  none  of  the  students  will  answer  all  of  the  questions  in  the 
time  allowed? Yes     No 

*Underline  the  answer  (Yes-No)  which  you  desire  to  make. 


6.  Is  it  your  custom  to  make  the  examination  short  enough  so  that 
practically  all  of  the  students  will  answer  all  of  the  questions  in  the  time 
allowed? Yes    No 

7.  If  you  have  given  an  affirmative  answer  to  Question  6,  do  you  note 

the  time  each  student  spends  in  writing  his  answers? Yes     No 

8.  What  proportion  of  the  final  mark  for  the  semester  is  based  upon 

the  final  written  examination  grade? % 

9.  In  assigning  grades  to  examination  papers  do  you  attempt  to  have 
their  distribution  conform  to  any  standard  form  such  as  the  normal  dis- 
tribution?      Yes     No 

10.  Do  you  usually  grade  all  the  answers  on  one  paper  before  taking 

up  those  of  another  paper? Yes     No 

11.  Do  you  usually  grade  the  answers  to  one  question  on  all  of  the 

papers  before  taking  up  the  answers  to  a  second  question? Yes     No 

12.  Instead  of  marking  the  answers  to  each  question  separately  do 

you  attempt  to  estimate  the  value  of  the  paper  as  a  whole? Yes     No 

13.  Before  starting  to  grade  a  set  of  examination  papers  do  you  write 

out  the  answers  which  you  consider  correct? Yes     No 

14.  When  you  consider  the  questions  of  an  examination  to  be  un- 
equal in  difficulty  is  it  your  practise  to  give  more  credit  for  a  correct  an- 
swer to  a  difficult  question  than  for  a  correct  answer  to  an  easy  question?     Yes     No 

15.  Approximately  how  much  time  do  you  use  in  marking  the  papers 
of  a  final  examination  which  the  students  are  allowed  a  total  of  90  min- 
utes for  answering?  Estimate  as  accurately  as  possible.  Base  this  answer 

on  a  class  of  25  students Min. 

16.  In  marking  examination  papers  do  you  intentionally  lower  a  stu- 
dent's mark  in  the  case  of 

(a)  poor  writing Yes     No 

(b)  poor  spelling Yes    No 

(c)  poor  English Yes     No 

17.  In  the  case  of  questions  which  are  essentially  mathematical  in 
character  do  you  give  credit  to  the  student  for  using  the  correct  principle 

even  though  the  final  answer  be  wrong? Yes     No 

NOTE:     It  is  desired  that  only  teachers  of  mathematics,  physics,  and  chemistry  answer  No.  17. 


NOTE  TO  TEACHER:    When  you  have  answered  the  above  questions  please  return  this  ques- 
tionnaire to  your  principal. 

[67] 


(Questionnaire  Sent  to  High-School  Principals) 

Principal High City 

1.  Do  you  require  your  teachers  to  give  final  examinations  at  the 

end  of  each  semester? Yes     No* 

("Final  examination"  as  used  in  this  questionnaire  means  an  ex- 
amination which  is  given  at  the  end  of  a  semester  and  which  is  based  on 
the  work  of  the  entire  semester) 

If  a  negative  answer  is  given  to  the  first  question,  no  answer  is  ex- 
pected for  the  remaining  questions. 

2.  a.  Is  it  the  practise  in  your  school  to  exempt  certain  students 

from  final  examinations? Yes     No 

b.  If  so,  what  are  the  conditions  (requirements)  upon  which  you 
base  exemption? 

1.  Deportment Yes    No 

2.  Scholarship Yes     No 

Other  requirements. 

3.  How  many  minutes  do  you  allow  for  final  written  examinations? Min. 

4.  Because  final  examinations  have  proven  unreliable  some  educators 
urge  that  students  be  given  more  than  one  comprehensive  examination 
in  each  subject,  and  that  these  examinations  be  given  on  different  days. 
Do  you  require  more  than  one  such  final  written  examination  in  each  sub- 
ject?      Yes    No 

5.  a.  In  marking  examination  papers  is  it  the  practise  in  your  school 

for  the  teachers  to  subtract  from  a  pupil's  grade  for 

1.  poor  writing Yes  No 

2.  poor  spelling Yes  No 

3.  poor  English Yes  No 

b.  Are  your  teachers  accustomed  to  giving  more  credit  for  correct 
answers  to  difficult  questions  than  for  correct  answers  to  easy 
questions? Yes     No 

c.  Is  it  the  practise  of  your  teachers  when  computing  a  semester 
mark  to  add  or  deduct  credit  in  proportion  to  the  time  used 

by  a  pupil  in  answering  the  final  written  examination  questions?  Yes     No 

6.  a.  Have  you  advised  your  teachers  as  to  what  proportion  of  the 

final  mark  for  the  semester  should  be  based  on  the  final  written 
examination? Yes    No 

b.  Have  you  made  a  definite  requirement  in  this  respect? Yes     No 

c.  If  so,  what  proportion  of  the  final  mark  for  the  semester  do  you 

require  to  be  based  upon  the  final  written  examination  mark? % 

7.  Additional  information  pertaining  to  this  topic  is  called  for  in  a 
a  second  questionnaire  which  is  to  be  filled  out  by  high  school  teachers. 
Would  you  be  willing  to  distribute  this  questionnaire  among  your  teach- 
ers?  If  so,  will  you  kindly  indicate  the  number  of  teachers  in  your  high 

school? 

♦Underline  the  answer  (Yes-No)  which  you  desire  to  malie. 

[68] 


EXAMPLES  OF  "NEW  EXAMINATIONS" 

(The  following  "new  examinations"  are  given  for  purposes  of  illustration.  They  may  in- 
clude several  exercises  which  will  prove  unsuitable  when  given  to  pupils.) 

TRUE-FALSE  EXAMINATION  IN  PHYSIOLOGY 

Prepared  by 

Bureau  of  Educational  Research 

University  of  Illinois 


Name Boy  or  Girl 

Age  last  birthday Next  birthday  will  be 

Grade Date City State. 

School Teacher 


.19. 


Below  you  will  find  a  number  of  statements.  Some  of  these  statements  are  true, 
others  are  not  true.  Read  each  statement  carefully,  then  if  it  is  true  mark  a  plus  (+) 
in  the  column  to  the  right  of  the  sentence.  If  the  statement  is  not  true  mark  a  minus 
(— )  in  the  column  to  the  right. 

EXAMPLES 

Read  the  statement  below  very  carefully. 


1.  Fats  will  form  a  lasting  mixture  with  water. 

This  is  not  a  true  statement  so  you  will  place  a  minus  (  — )  sign  in  the 
column.     Now  read  the  second  sentence. 

2.  The  layer  of  fat  just  beneath  the  skin  is  more  than  one- 
tenth  of  an  inch  thick. 

This  is  a  true  statement  so  you  will  mark  a  plus  (+)  sign  in  the  column. 
Now  read  the  third  sentence. 

3.  The  union  of  oxygen  with  any  substance  produces  heat. 

This  is  a  true  statement  so  you  will  mark  a  plus  (+)  sign  in  the  column. 
Now  read  the  fourth  sentence. 

4.  Nitrogen  constitutes  only  one-fifth  of  the  volume  of  the  air, 

This  is  a  false  statement  so  you  will  mark  a  minus  (  — )  sign  in  the 
column 


Answers  to  be 
written  here 


[69] 


PHYSIOLOGY 

1.  The  kidneys  vary  12  inches  to  16  inches  in  length. 

2.  The  external  poisoning  of  the  skin  by  poison  ivy  or  sumac  never 
results  seriously. 

3.  A  person  having  a  good  mind  must  necessarily  have  a  large  brain. 

4.  Color  blindness  is  more  prominent  in  men  than  women. 

5.  Plenty  of  fluids  should  be  drunk  at  the  time  of  eating  solid  food. 

6.  Bones  are  composed  of  animal  and  mineral  matter. 

7.  The  nails  are  hardened  outer  skin  or  epidermis. 

8.  The  use  of  alcohol  increases  the  tendency  to  commit  crime. 

9.  A  full  grown  person  contains  about  six  quarts  of  blood. 

10.  The  brain  is  almost  perfectly  spherical  in  shape. 

11.  The  kidneys  are  almost  perfectly  round. 

12.  All  animals  are  made  up  of  cells. 

13.  Substances,  like  glass,  which  permit  rays  of  light  to  pass  through 
them  readily  are  said  to  be  opaque. 

14.  The  sense  organs  of  smell  are  located  in  the  lining  of  the  cavity  of 
the  nose. 

15.  The  skin  is  composed  of  two  layers  of  tissue. 

16.  The  end  organs  for  taste  occur  in  the  mucous  membrane  of  the 
tongue. 

17.  To  extinguish  the  burning  clothing  of  a  person,  it  is  necessary  to 
wrap  him  in  something  to  exclude  the  air. 

18.  All  of  the  interior  of  the  spinal  cord  is  filled  with  gray  matter  con- 
taining nerve  cells. 

19.  The  great  difference  in  the  complexion  of  persons  is  due  largely 
to  the  pigment  lying  in  the  epidermis. 

20.  Cancer  is  caused  by  germs  growing  in  the  tissue. 

[70] 


Answers  to  be 
written  here 


21.  Diphtheria  can  be  controlled  by  the  use  of  Diphtheria  antitoxin. 

22.  The  brain  is  separated  into  two  parts  or  hemispheres  by  a  great 
longitudinal  fissure. 

23.  When  oxygen  is  separated  from  other  substances  the  process  is 
called  oxidation. 

24.  Infectious  diseases  are  due  to  changed  methods  of  work  and 
growth  on  the  part  of  cells  in  certain  regions  of  the  body. 

25.  The  use  of  alcoholic  beverages  builds  up  the  body  and  makes  the 
muscles  stronger. 

26.  The  great  majority  of  grown  people  have  been  infected  with 
tuberculosis  germs. 

27.  The  sense  organs  are  the  terminations  of  the  sensory  nerves  serv- 
ing to  carry  impressions  to  the  spinal  cord  or  brain. 

28.  Farsightedness  is  often  caused  by  a  blow  on  the  eye. 

29.  An  antiseptic  is  a  substance  which  merely  restrains  the  germs  from 
growing. 

30.  The  brain  is  in  communication  with  the  rest  of  the  body  by  means 
of  nerves. 

31.  The  cerebrum  is  the  path  of  communication  between  the  nerves 
supplying  the  arms,  trunk,  legs,  and  brain. 

32.  The  chief  function  of  muscles  is  to  hold  up  the  body. 

33.  All  milk  contains  bacteria. 

34.  The  alcohol  used  in  drinks  is  produced  by  the  growth  of  yeast  in  a 
liquid  containing  sugar. 

35.  Our  blood  contains  white  corpuscles  which  destroy  disease  germs. 

36.  More  people  die  daily  from  diphtheria  than  from  tuberculosis. 

37.  The  use  of  tobacco  increases  the  strength  of  the  muscles. 

38.  The  use  of  tobacco  makes  the  nerve  cells  function  more  keenly, 

39.  The  chewing  of  dry  bread  aids  the  digestion  as  much  as  the  use  of 
gum. 

[71] 


Answers  to  be 
written  here 


Answers  to  be 
written  heie 


A 


40.  Air  is  composed  chiefly  of  two  gases,  oxygen  and  nitrogen. 

41.  The  first  step  in  treating  a  person  who  has  been  poisoned  is  to 
give  an  emetic. 

42.  Light  is  produced  by  waves  of  a  substance  called  ether. 

43.  Non-infectious  diseases  are  caused  by  small  plants  or  animals 
called  parasites  feeding  upon  the  human  body. 

44.  Alcoholic  beverages  have  great  value  in  curing  disease. 

45.  A  drink  of  alcoholic  beverage  in  the  winter  time  causes  a  man's 
body  to  become  warm. 

46.  Each  portion  of  the  brain  has  its  own  definite  work  to  perform. 

47.  Fainting  is  caused  by  an   over-sufficient  supply  of  blood  being 
sent  to  the  brain. 

48.  The  spinal  cord  may  act  independently  of  the  brain  and  produce 
many  of  the  muscular  movements  necessary  in  routine  work. 

49.  The  germs  of  typhoid  fever  usually  gain  access  to  the  body  by 
being  breathed  in  with  air. 

50.  Narcotics  are  substances  which  cause  any  organs  of  the  body  to 
act  more  vigorously  than  is  their  custom. 


Directions  to  teachers:  After  the  four  examples  have  been  studied  by  the 
pupils,  read  the  following  directions  to  them:  "On  the  next  page  you  will  find  a  num- 
ber of  statements  similar  to  the  ones  you  have  just  read.  You  are  to  place  a  plus  sign 
or  a  minus  sign  in  the  column  to  the  right  of  each  statement  just  as  has  been  done  on 
the  first  page.  Mark  all  of  the  statements  that  you  are  sure  you  can  answer  corrertly. 
If  you  find  a  statement  that  you  are  not  sure  you  can  answer  correctly,  study  It  care- 
fully and  then  mark  the  answer  you  think  will  be  correct.  If  you  find  a  statement  you 
know  nothing  about,  make  no  attempt  to  mark  it,  as  guessing  counts  heavily  against 
you.  You  will  have  25  minutes  for  the  test.  I  shall  expect  you  to  stop  promptly  and 
turn  your  folders  face  down  on  the  desk  when  I  tell  you  to  do  so.    Ready-Go." 

In  computing  the  score  of  each  pupil  on  a  test  subtract  the  total  number  of  wrong 
answers  from  the  total  number  of  right  answers.  Such  scores  are  called  "point-scores." 
In  interpreting  them  it  is  advisable  to  form  a  distribution  which  will  show  how  many 
pupils  received  each  score.  From  the  distribution  it  is  possible  to  work  out  a  basis  for 
translating  the  point  scores  into  the  usual  kind  of  school  marks. 


NOTE:     The    "Directions  to   teachers"    given    above    would    not   appear   on   the    usual   printed 
examinations.     They    are    placed    here    for    the    convenience  of  teachers. 


[72] 


COMPLETION  EXAMINATION  IN  AMERICAN  GOVERNMENT 

Prepared  by 

Bureau  of  Educational  Research 

University  of  Illinois 


Name Boy  or  Girl 

Age  last  birthday Next  birthday  will  be 19. 

Grade Date City State 

School Teacher 


Below  you  will  find  a  number  of  statements.  In  each  statement  one  or  more  im- 
portant words  have  been  omitted.  Each  blank  in  the  sentence  shows  where  a  word 
has  been  left  out.  Read  each  statement  carefully,  then  write  in  the  blank  the  word 
which  completes  the  meaning  of  the  statement.  You  will  be  allowed  15  minutes  for 
the  test. 

1.  The  primary  purpose  for  which  government  exists  is  the of  our  lives 

and  property. 

2.  Citizenship  may  be  acquired  by in  this  country  or  by  a  process  of 

for  natives  of  other  lands. 

3.  Our  national  government  derives  its  authority  from  the of  the  United 

States  through  our  national 

4.  The  legislative  power  granted  to  the  national  government  is  vested  in  a  Congress  of 

houses,  the  smaller  of  which  is  called  the and  the 

larger  the 

5.  The  execution  of  the  laws  made  by is  intrusted  to  the 

of  the  United  States. 


6.  All  judges  connected  with  the  national  courts  are  appointed  for  life  with  the  consent 
of 

7.  Most  of  the  candidates  for  office  which  are  filled  by  popular  vote  are  nominated 
directly  in 

8.  The  Fifteenth  Amendment  of  the  United  States  Constitution  prevents  the  states 

from  denying  to  citizens  the  right  to  vote  on  account  of , 

,  or  previous  condition  of 

[73] 


9.  Practically  all  of  our  law-making  bodies  are  made  up  of. chosen 

for  short  terms  from into  which  the  states,  counties  and    cities  are 

divided. 

10.  The  first  permanent  English  settlements  in  America  were  made  in  what  is  now  the 
state  of 

11.  In  a  county,  the  records  of  the  county  board  and  other  official  papers  are  preserved 
by  the  counts' 

12.  All  cities  are  public  corporations  created  under municipal  laws. 

13.  Ever>'  incorporated  city  obtains  from  the government  a 

under  which  it  may  elect  its  officials  and  conduct  its  business. 

14.  Civil  service  employees  may  be  removed  from  service  only  for 

15.  The  power  of  Impeaching  a  state  officer  is  given  to  the 

16.  The is  by  far  the  most  prominent  and  powerful  executive  official 

in  the  state.     Ver)' state  officers  are  appointed  by  him  or  are  re- 
sponsible to  him. 

17.  All  important  officials  connected  with  the  executive  or  judicial  service  of  the 

United  States  may  be  removed  by through  the  lower  house  of 

Congress  and  by in  the  senate. 

18.  Far  more  property  is  destroyed  by than  by  all  other  agencies. 

19.  There  is  no  task  of  state  and  local  government  which  outranks  in  importance  that 
of  providing  an education  at  public  expense. 

20.  All  rivers  and  canals  within  a  single  state  are  controlled  by  the 

in  which  they  are  located. 

21.  Most  of  the  revenue  for  state  and  local  governments  is  secured  by  a 

on 

22.  A  state is  the  fundamental  law  which  the  people  of  the  state  have 

arranged  for  their  government  and  protection. 

23.  A  state  constitution  can  be  changed  by  means  of  an 

24.  The  three-fifths  compromise  provided  that  five should  be  counted  as 

equal  to  three when  reckoning  the for  either  direct 

taxation  or  representation. 

[74] 


RECOGNITION  EXAMINATION  IN  ALGEBRA 

Prepared  by 

Bureau  of  Educational  Research 

University  of  Illinois 


Name Boy  or  Girl 

Age  last  birthday Next  birthday  will  be 19. 

Grade Date City State 

School Teacher 


Below  you  will  find  a  number  of  statements.  In  each  statement  a  word  or  number 
has  been  omitted.  At  the  close  of  the  statement  several  words  or  numbers  have  been 
given.  One  of  these  is  the  correct  answer.  Select  the  word  or  number  which  you  think 
is  correct  and  draw  a  line  under  it.  Most,  if  not  all,  of  the  examples  can  be  solved  by 
mental  calculation.  If  any  figuring  is  necessary,  work  on  the  margin  of  the  page. 
You  will  be  allowed  17  minutes  for  the  test. 

1.  Numbers  that  are  represented  by  letters  are  called numbers. 

substituted — literal 

2.  When  two  or  more  letters  are  multiplied  together  each  is  called  a 

of  the  product.  factor — coefficient 

3.  If  a  man  rides  a  certain  distance  in  10  hours,  in  h  hours  he  rides 


4.  The  statement  2x  +  5  =  29  is  called  an identity — equation. 

5.  If  16  is  subtracted  from  three  times  a  certain  number  the  result  is  1 10.      The  number 
is 36^;  31M;  42 

6.  A  number  which  is  a  factor  of  two  or  more  numbers  is  called  a factor. 

common — equ  al 

7.  If  there  are  two  equal  factors  of  a  number,  either  is  called  the of  the 

number.  square  root — common  factor 

8.  To  multiply  algebraic  fractions  take  the of  the  numerators  for  a 

new  numerator  and  the  product  of  the  denominators  for  a  new  denominator, 
sum — product 

[75] 


9.  A  fraction  whose  numerator  or  denominator  (or  both)  contains  fractions  is  called  a 
fraction.  multiple — complex 

10.  A is  a  statement  of  a  fact  which  is  to  be  proved,   theorem — axiom 

11.  The  name  given  the  +  sign  is negative — positive 

12.  To  find  the  sum  of  two  numbers  whose  signs  are  opposite,  take  their 

regarding  each  as  positive,  and  prefix  the  sign  of  the  larger  number  to  the  answer, 
sum — difference — product 

13.  Whenever  a  number  occurs  without  a  sign,  the sign  is  to  be  under- 
stood.                      X;  +;  — 

14.  The  number  denoting  the  power  of  a  term  is  called  the 

prefix — exponent 

15.  If  a  =  2,  b  =  -  3,  and  c  =  -  5  then^^  = -  6;  -  2;  30 

a 

16.  In  adding  like  terms  add  the  coefficients  for  the  new  coefficient  and 

it  by  the  common  factor.  multiply — divide 

17.  An  expression  which  contains  more  than  one  term  is  called  a 

monomial — polynomial 

18.  If  the  length  of  a  rectangle  =4  feet  more  than  twice  the  width,  the  perimeter  = 
56  feet.     The  length  = feet.  8—12—16 

19.  Any  term  may  be  transposed  from  one  side  of  an  equation  to  the  other,  provided 
its  is  changed.  sign — value 

20.  Any  equation  which  contains  no  higher  power  of  the  unknown  letter  than  the  first 
is  called  a equation.  radical — simple 

21.  The  exponent  of  the  product  of  two  powers  of  the  same  number  is  equal  to  the 
of  the  exponents  of  the  factors.  product — sum 

22.  To  raise  the  product  of  two  numbers  to  any  power,  raise  the  numbers  separately 
to  that  power  and  take  their product — sum 

23.  The  square  of  any  two  numbers  is  equal  to  the  square  of  the  first  number 

twice  the  product  of  the  two  plus  the  square  of  the  second  number,  plus — minus 

24.  A  20  foot  ladder  rests  against  a  building,  the  bottom  of  the  ladder  being  12  feet 
from  the  cellar  wall.    The  top  is feet  from  the  ground.  8-16 

25.  In  division,  the  sign  of  the  quotient  is whenever  the  dividend  and 

divisor  have  like  signs.  — ;  + 

[76] 


26.  In  finding  the  quotient  of  two  powers  of  the  same  number  the  exponent  of  the 

quotient  is  equal  to  the  exponent  of  the  dividend by  that  of  the  divisor. 

increased — diminished 

27.  (3x2-2x-l)-^(x-l)  = 3x+l;3x-l 

28.  A  factor  which  has  no  factor  except  itself  and  unity  is  called  a factor. 

prime — multiple 

29.  The  product  of  all  the  common  prime  factors  of  two  or  more  numbers  or  expres- 
sions is  called  their common  factor.  highest — lowest 

30.  If  one  number  is  exactly  divisible  by  another,  the  first  is  called  a of  the 

second.  divisor — multiple 

31.  In  algebraic  fractions  the  dividend  is  called  the 

denominator — numerator 


[77] 


UNIVERSITY    OF    ILLINOIS    BULLETIN 

Issued  Weekly 
Vol.  XXI  November  26,  1923  No.  13 

[Entered  as  second-class  matter  December  11,  1912,  at  the  post  office  at  Urbana,  Illinois,  under  the 
Act  of  August  24,  1912.  Acceptance  for  mailing  at  the  special  rate  of  postage  provided  for  in 
secticQ   1103,  Act  of  October  3,   1917,  authorized  July  31,    1918.] 


BULLETIN  No.  17 


BUREAU  OF  EDUCATIONAL  RESEARCH 
COLLEGE  OF  EDUCATION 

THE  PRESENT 
STATUS  OF  WRITTEN  EXAMINATIONS 
AND  SUGGESTIONS  FOR  THEIR  v^ 
IMPROVEMENT 


By 


Walter  S.  Monroe 
Director,   Bureau  of  Educational  Research 

Assisted  by 

Lloyd  B.  Souders 
Formerly  Assistant  in   Bureau  of  Educational  Research 


PRICE    50   CENTS 


PUBLISHED  BY  THE  UNIVERSITY  OF  ILLINOIS,  URBANA 

1923 


The  Bureau  of  Educational  Research  was  established  by  act 
of  the  Board  of  Trustees  June  1,  1918.  It  is  the  purpose  of  the 
Bureau  to  conduct  original  investigations  in  the  field  of  education, 
to  summarize  and  bring  to  the  attention  of  school  people  the  results 
of  research  elsewhere,  and  to  be  of  service  to  the  schools  of  the 
state  in  other  ways. 

The  results  of  original  investigations  carried  on  by  the  Bureau 
of  Educational  Research  are  published  in  the  form  of  bulletins.  A 
complete  list  of  these  publications  is  given  on  the  back  cover  of 
this  bulletin.  At  the  present  time  five  or  six  original  investigations 
are  reported  each  year.  The  accounts  of  research  conducted  else- 
where and  other  communications  to  the  school  men  of  the  state 
are  published  in  the  form  of  educational  research  circulars.  From 
ten  to  fifteen  of  these  are  issued  each  year. 

The  Bureau  is  a  department  of  the  College  of  Education.  Its 
immediate  direction  is  vested  in  a  Director,  who  is  also  an  instructor 
in  the  College  of  Education.  Under  his  supervision  research  is 
carried  on  by  other  members  of  the  Bureau  staff  and  also  by  grad- 
uates who  are  working  on  theses.  From  this  point  of  view  the 
Bureau  of  Educational  Research  is  a  research  laboratory'  for  the 
College  of  Education. 

Bureau  of  Educational  Research 

College  of  Education 

University  of  Illinois,  Urbana 


THE  UNIVERSITY  OF  ILLINOIS 

THE  STATE  UNIVERSITY 

URBANA 

DAVID  KINLEY,  PhD.,  LL.D.,  President 


The  University  Includes  the  Follozoing  Departments 

The  Graduate  School 

The  College  of  Liberal  Arts  and  Sciences  (Ancient  and  Modern  Languages 
and  Literatures;  History,  Economics,  Political  Science,  Sociology,  Philosophy, 
Psychology,  Education;  Mathematics;  Astronomy;  Geology;  Physics;  Chemistry; 
Botany,  Bacteriology,  Zoology,  Entomology;  Physiology;  Art  and  Design;  Home 
Economics) 

The  College  of  Commerce  and  Business  Administration  (General  Business, 
Banking,  Insurance,  Accountancy,  Railway  Administration,  Railway  Transpor- 
tation, Industrial  Administration,  Foreign  Commerce;  Courses  for  Commercial 
Teachers  and  Commercial  and  Civic  Secretaries;  Commerce  and  Law) 

The  College  of  Engineering  (Architecture;  Architectural,  Ceramic,  Civil,  Elec- 
trical, Gas,  General,  Mechanical,  Mining,  Municipal  and  Sanitary,  Railway  En- 
gineering, and  Engineering  Physics) 

The  College  of  Agriculture  (Agronomy;  Animal  Husbandry;  Dairy  Husbandry; 
Farm  Mechanics,  Farm  Organization  and  Management;  Horticulture,  Landscape 
Gardening,  and  Floriculture;  Agricultural  Extension;  Home  Economics) 

The  College  of  Law  (Three-year  and  four-year  curriculums  based  on  two  years  of 
college  work) 

The  College  of  Education  (General  Education;  Athletic  Coaching;  Agricultural 
Education;  Home  Economics  Education;  Industrial  Education;  Music  Educa- 
tion; University  High  School;  Bureau  of  Educational  Research) 

The  Curriculum  in  Journalism 

The  Curriculums  in  Chemistry  and  Chemical  Engineering 

The  School  of  Railway  Engineering  and  Administration 

The  School  of  Music  (four-year  curriculum) 

The  Library  School  (two-year  curriculum  for  college  graduates) 

The  College  of  Medicine  (in  Chicago) 

The  College  of  Dentistry  (in  Chicago) 

The  School  of  Pharmacy  (in  Chicago;  Ph.G.  and  Ph.C.  curriculums) 

The  Summer  Session  (eight  weeks) 

EIxperiment  Stations  and  Scientific  Bureaus:  U.  S.  Agricultural  Experiment 
Station;  Engineering  Experiment  Station;  State  Natural  History  Survey;  Bio- 
logical Experiment  Station  on  Illinois  River;  State  Water  Survey;  State  Geolog- 
ical Survey;  U.  S.  Bureau  of  Mines  Experiment  Station. 

The  library  collections  contain  July  1,   1923,  556,105  volumes  and  127,941  pam- 
phlets. For  catalogs  and  information  address 

THE  REGISTRAR 

Urbana,  Illinois 


BULLETINS  OF  THE  BUREAU  OF  EDUCATIONAL  RESEARCH 

COLLEGE  OF  EDUCATION,  UNIVERSITY  OF  ILLINOIS, 

URBANA,  ILLINOIS 

Price 
No.  1.    Buckingham,  B.  R.    Bureau  of  Educational  Research,  Announcement, 

1918-19 IS 

No.  2.   First  Annual  Report 25 

No.  3.  Bamesberger,  Velda  C.  Standard  Requirements  for  Memorizing  Lit- 
erary   Material SO 

No.  4.   Holley,  Charles  E.  Mental  Tests  for  School  Use.    (Out  of  print) SO 

No.  5.   Monroe,  Walter  S.  Report  of  Division  of  Educational  Tests  for  1919-20      .25 

No.  6.   Monroe,  Walter  S.   The  Illinois  Examination 50 

No.  7.  Monroe,  Walter  S.  Types  of  Learning  Required  of  Pupils  in  the  Sev- 
enth and  Eighth  Grades  and  in  the  High  School 15 

No.  8.   Monroe,  Walter  S.  A  Critical  Study  of  Certain  Silent  Reading  Tests..       .50 

No.  9.   Monroe,  Walter  S.  Written  Elxaminations  and  Their  Improvement 50 

No.  10.    Bureau  of  Educational  Research.   Relation  of  Size  of  Class  to  School 

Efficiency SO 

No.  11.   Monroe,  Walter  S.  Relation  of  Sectioning  a  Class  to  the  Effectiveness 

of  Instruction 15 

No.  12.    Odell,  Charles  W.  The  Use  of  Intelligence  Tests  as  a  Basis  of  School 

Organization   and   Instruction 50 

No.  13.   Monroe,  Walter  S.,  and  Foster,  I.  0.  The  Status  of  the  Social  Sciences 

in  the  High  Schools  of  the  North  Central  Association SO 

No.  14.  Monroe,  Walter  S.,  and  Carter,  Ralph  E.  The  Use  of  Different  Types 
of  Thought  Questions  in  Secondary  Schools  and  Their  Relative  Dif- 
ficulty for  Students 30 

No.  15.   Monroe,  Walter  S.  The  Constant  and  Variable  Errors  of  Educational 

Measurements 25 

No.  16.  Odell,  Charles  W.  An  Annotated  Bibliography  Dealing  With  the 
Classification  and  Instruction  of  Pupils  to  Provide  for  Individual 
Differences SO 

No.  17.  Monroe,  Walter  S.,  and  Souders,  Lloyd  B.  Present  Status  of  Writ- 
ten Examinations  and  Suggestions  for  Their  Improvement 50 


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